tag:blogger.com,1999:blog-99597762024-03-08T02:07:40.792+00:00James' Empty BlogIf I have seen further than others, it is by treading on the toes of giantsJames Annanhttp://www.blogger.com/profile/04318741813895533700noreply@blogger.comBlogger2374125tag:blogger.com,1999:blog-9959776.post-56597033076687399022023-12-14T13:10:00.003+00:002023-12-14T13:13:36.138+00:00 Vallance vs Vallance vs SAGE: Edmunds’ view<p><span face="Helvetica, sans-serif" style="color: #494949; font-size: 13px; text-align: justify;">I’ve mainly focussed on Vallance, partly because he was the Govt’s Chief Scientific Advisor and also co-Chair of SAGE (along with Whitty) but also because he’s had the most to say, and been the most clearly wrong in what he did say. But it’s also interesting to compare and contrast with other prominent members of SAGE. Prof John Edmunds is one such, I probably don’t need to show his horrendous TV interview of the 13th of March again but will do so anyway. It’s so endearing to see him sneering at Tomas Pueyo after the latter informs him correctly that the doubling time of the pandemic is about 3 days and a catastrophe is unfolding under out noses. No, he replies, you just don’t understand the data, the doubling time is really 5 days, and we mustn’t act too soon (go to 23:15 in the video):</span></p><p></p><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="266" src="https://www.youtube.com/embed/C98FmoZVbjs" width="320" youtube-src-id="C98FmoZVbjs"></iframe></div><br /><span face="Helvetica, sans-serif" style="color: #494949; font-size: 13px; text-align: justify;"><br /></span><p></p><div style="color: #494949; font-family: Helvetica, sans-serif; font-size: 13px; text-align: justify;"><figure class="wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio"><div class="wp-block-embed__wrapper"></div></figure><p>In his recent testimony to the Inquiry, Edmunds says:</p><blockquote class="wp-block-quote is-layout-flow wp-block-quote-is-layout-flow"><p><em>the surveillance system was poor, with the data being delayed and hard to interpret – so much so, that estimating the growth rate of the epidemic was difficult (estimates of the doubling time varied from about 3 days to about 5-7 days, depending on what method and data sources were used) and getting an accurate assessment of the overall size of the epidemic was also difficult. The delays and under-reporting (partly due to a lack of testing) might well have led decision-makers to conclude that they had more time to act than was the case.</em></p></blockquote><p>It would have been more honest of him to say that <em>his interpretation of the data</em> was poor (along with the rest of SAGE) and this lead decision makers to believe they had more time to act. Furthermore, including the estimate of 3 day doubling in that comment above is particularly misleading, as SAGE was not acknowledging the legitimacy of such estimates at the time. Indeed he ridiculed the number when Pueyo suggested in on the evening of 13th March. But this post isn’t really about SAGE’s competence, it is just about establishing what SAGE actually did say at the time.</p><p>Edmunds then goes on to say:</p><blockquote class="wp-block-quote is-layout-flow wp-block-quote-is-layout-flow"><p><em>Surveillance started to improve after the CHESS (‘COVID-19 Hospitalisation in England Surveillance System’) system was launched in hospitals on around 14-15th March, but it took a little while for the new data-stream to stabilise.</em></p></blockquote><p>Here we see clear blue water between his testimony and that of Vallance. Remember, Vallance talks of SAGE members having a Road to Damascus conversion over the weekend of 14-15 March due to this new data becoming available. Edmunds does not repeat that claim, presumably because he knows it to be false. Perhaps he does not, however, contradict Vallance quite clearly enough for this contradiction to be obvious to a casual reader – or even those undertaking the Inquiry. He then rapidly passes on to the responsibility decision-makers had for deciding what to do. He admits that “<em>It is certainly possible that had SAGE been earlier, clearer and more urgent in its advice then lockdown could have been introduced earlier</em>.” “<em>Earlier, clearer and more urgent</em>” indeed. He could have added “<em>correct</em>“. But he didn’t.</p></div>James Annanhttp://www.blogger.com/profile/04318741813895533700noreply@blogger.com0tag:blogger.com,1999:blog-9959776.post-85184412895020155952023-11-28T16:40:00.000+00:002023-11-28T16:40:48.890+00:00 Vallance vs Vallance vs SAGE: Letter to the UK Covid-19 Inquiry<p><span style="color: #494949; font-family: Helvetica, sans-serif; font-size: 13px; text-align: justify;">I’ve sent the following letter to the Public Inquiry, noting the significant and repeated inconsistencies between what Vallance has recently testified about the events in mid-March 2020, and what the contemporaneous documentary evidence of that period actually says. This evidence includes, rather amusingly, Vallance himself in one of the daily PM statements and press conferences. I will of course post any response(s) received.</span></p><div style="color: #494949; font-family: Helvetica, sans-serif; font-size: 13px; text-align: justify;"><p></p><p>To: contact@covid19.public-inquiry.uk</p><p>To whom it may concern.</p><p>I have noticed a discrepancy between the witness statements made to the Inquiry by Sir Patrick Vallance concerning the events of March 2020, and documentary evidence from that period. It primarily concerns the estimation of the doubling time of the pandemic, which was of great importance in planning the policy response to it. The reason why this is important is that changing the estimate of doubling time from 5 days to 3 days would indicate that the problem was far greater, more urgent, and harder to deal with, than was previously thought. It would inevitably lead to an abrupt and urgent change in policy requirements. However, there is no evidence to support the claim made by Vallance that SAGE was calling for urgent and strict action from March 16 onwards, and that the Govt delayed action for a further week.</p><p><strong>Vallance’s evidence to the UK Covid-19 Inquiry</strong></p><p>To the Inquiry, Vallance stated that he, and other members of SAGE, changed their minds about the growth rate of the pandemic over the weekend of 14-15 March (bold emphasis added by me):</p><p>“I think the new understanding on the weekend of 14 and 15 March was that we were much further ahead in the pandemic than we realised, and the numbers that came in that week showed that there were many more cases, it was far more widespread, and <strong>was accelerating faster than anyone had expected</strong>.”</p><p>“We got information on 13 March which unambiguously showed that the pandemic was far more widespread and far bigger and <strong>moving faster than we had anticipated</strong>“</p><p>“The advice given on 18 March was a consequence of our concerns about the <strong>rapid doubling time</strong> and number of infections”</p><p>“A major reason SAGE did not advise earlier and more extensive interventions, for example on 10 March rather than 16 March, was that we were unaware of how widely seeded the virus was in the UK and <strong>how short the doubling time had become</strong>.”</p><p>“I am asked if the models underestimated the spread of the virus early in the pandemic. I think that they did, at least in terms of speed until shortly before the four day period of 13 to 16 March, which I discuss above. This was a function of poor and time delayed data and a consequent <strong>under-estimation of the virus’ doubling time</strong>.”</p><p>The conclusions that we are inescapably being asked to draw from these multiple statements is that (a) SAGE was underestimating the growth rate of the pandemic prior to the weekend of 14/15 March, but corrected their error at that time and (b) the correction of this error was critical in changing their advice from a measured program of mitigation to a much more urgent suppression of the pandemic.</p><p><strong>Vallance’s evidence to the House of Commons Science and Technology Committee, July 2020</strong></p><p>This mirrors the testimony Vallance gave previously to the House of Commons Science and Technology committee in July 2020:</p><p>“When the SAGE sub-group on modelling, SPI-M, saw that <strong>the doubling time had gone down to three days</strong>, which was in the middle of March, that was when the advice SAGE issued was that the remainder of the measures should be introduced as soon as possible.”</p><p>“The advice changed <strong>because the doubling rate of the epidemic was seen to be down to three days instead of six or seven days</strong>. We did not explicitly say how many weeks we were behind Italy as a reason to change; it was the doubling time, and the realisation that, on the basis of the data, we were further ahead in the epidemic than had been thought by the modelling groups up until that time.”</p><p><strong>SAGE minutes of mid-March and other contemporaneous evidence</strong> </p><p>However, contrary to these claims, the minutes of the SAGE meeting on the 16th March very clearly stated:</p><p>“UK cases may be <strong>doubling in number every 5-6 days</strong>.”</p><p>and later that day, Vallance personally repeated the 5 day doubling figure live on TV:</p><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="266" src="https://www.youtube.com/embed/Eauc67Ba-8k" width="320" youtube-src-id="Eauc67Ba-8k"></iframe></div><br /><p><br /></p><figure class="wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio"><div class="wp-block-embed__wrapper"></div></figure><p>“…the epidemic, you’d expect to <strong>double every 5 days or so</strong>…”</p><p>Two days later, the minutes of the SAGE meeting on the 18th March again stated:</p><p>“<strong>Assuming a doubling time of around 5-7 days continues to be reasonable</strong>, but this is before any of the measures brought in have had an effect; these measures are likely to slow the doubling time even if there is still an exponential curve.”</p><p>The first time 3 day doubling was hinted at in any official documentation appears to be the SPI-M-O meeting on the 20th March:</p><p>“Nowcasting and forecasting of the current situation in the UK suggests that the <strong>doubling time of cases accruing in ICU is short, ranging from 3 to 5 days</strong>.”</p><p>and this was finally endorsed in the SAGE minutes of the 23rd March:</p><p>“<strong>The doubling time for ICU patients is estimated to be 3-4 days</strong>“</p><p>It looks like Sir Patrick may have confused the weekends of 14-15 March, with 21-22 March. For example, the SPI-M meeting he referred to above as taking place prior to SAGE’s change of heart “in the middle of March” is actually documented as having taken place on the 20th March. I hope you will be able to contact him to ask him about these discrepancies.</p><p>At the very least, the documentary evidence proves that SAGE was still underestimating the growth rate of the pandemic right through their meetings of the 16th and 18th March, only finally correcting their error on the 23rd. But perhaps a more worrying implication here is that Sir Patrick’s recollection of SAGE’s approach towards mitigation and lockdown at this time is also in error. In fact, the minutes of the meetings of the 16th and 18th appear entirely supportive of the Govt actions at that time, which were to continue with the gradual extension of the measured program of (mostly voluntary) measures. On the 16th:</p><p>“SAGE cannot be certain that the measures being considered by HMG will be sufficient to push demand for critical care below NHS capacity but they may get very close under the RWC scenario.</p><p>While SAGE’s view remains that school closures constitutes one of the less effective single measure to reduce the epidemic peak, it may nevertheless become necessary to introduce school closures in order to push demand for critical care below NHS capacity. However school closures could increase the risks of transmission at smaller gatherings and for more vulnerable groups as well as impacting on key workers including NHS staff. As such it was agreed that further analysis and modelling of potential school closures was required (demand/supply, and effects on spread).”</p><p>and on the 18th:</p><p>“SAGE advises that the measures already announced should have a significant effect, provided compliance rates are good and in line with the assumptions. Additional measures will be needed if compliance rates are low.”</p><p>They even argued that the measures implemented on the 18th (including the new school closures) were probably adequate to fully suppress the pandemic:</p><p>“SAGE reviewed available evidence and modelling on the potential impact of school closures. The evidence indicates that school closures, combined with other measures, could help to bring the R0 number below 1, although there is uncertainty.”</p><p><strong>Summary</strong></p><p>The claims that the Govt was responsible for a week of delay at this time, and that SAGE was arguing for much more immediate and stringent action, is not supported by a reasonable reading of the evidence. Indeed, SAGE had no reason to be doing this, since they still believed (contrary to Vallance’s testimony above) that the pandemic was doubling at a rate no more rapidly than 5 days (at worst) and furthermore, as they explicitly stated on the 18th, was probably being significantly slowed beyond this figure by existing policies already introduced at that time.</p><p>All of the quotations I have given above are directly copied from official documentation available on the Govt’s own web site, other than that taken from the youtube video of the PM statement and press conference of the 16th March which is my own transcription. Please contact me if you require any help in validating the provenance or accuracy any of this evidence.</p><p>Regards,</p><p>James Annan</p><p>jdannan@blueskiesresearch.org.uk</p></div>James Annanhttp://www.blogger.com/profile/04318741813895533700noreply@blogger.com2tag:blogger.com,1999:blog-9959776.post-58500258711609686302023-11-25T13:22:00.001+00:002023-11-25T13:22:20.713+00:00Vallance vs Vallance vs SAGE: Why does doubling time matter?<p><span style="color: #494949; font-family: Helvetica, sans-serif; font-size: 13px; text-align: justify;">One thing that all the protagonists (myself included) agree on is that SAGE’s estimate of doubling time in mid-March was of critical importance. Vallance</span><span style="color: #494949; font-family: Helvetica, sans-serif; font-size: 13px; text-align: justify;"> </span><a href="https://bskiesresearch.files.wordpress.com/2023/11/vallance_stc.pdf" style="font-family: Helvetica, sans-serif; font-size: 13px; text-align: justify;">testified forcefully to this effect in 2020</a><span style="color: #494949; font-family: Helvetica, sans-serif; font-size: 13px; text-align: justify;">:</span></p><div style="color: #494949; font-family: Helvetica, sans-serif; font-size: 13px; text-align: justify;"><blockquote class="wp-block-quote"><p><em>When the SAGE sub-group on modelling, SPI-M, saw that the doubling time had gone down to three days, which was in the middle of March, that was when the advice SAGE issued was that the remainder of the measures should be introduced as soon as possible.</em></p></blockquote><p>And then confirmed in this exchange with a committee member:</p><blockquote class="wp-block-quote"><p><em>Sir Patrick Vallance: Knowledge of the three-day doubling rate became evident during the week before. </em></p></blockquote><blockquote class="wp-block-quote"><p><em>Q1080 [ed – this number has changed from the previous time I posted about this] Graham Stringer: Did it immediately affect the recommendations on what to do? </em></p></blockquote><blockquote class="wp-block-quote"><p><em>Sir Patrick Vallance: It absolutely affected the recommendations on what to do, which was that the remaining measures should be implemented as soon as possible. I think that was the advice given.</em></p></blockquote><p>and again:</p><blockquote class="wp-block-quote"><p><em>Sir Patrick Vallance: The advice changed because the doubling rate of the epidemic was seen to be down to three days instead of six or seven days. We did not explicitly say how many weeks we were behind Italy as a reason to change; it was the doubling time, and the realisation that, on the basis of the data, we were further ahead in the epidemic than had been thought by the modelling groups up until that time.</em></p></blockquote><p>But why does the doubling time matter so much, and is the difference between 3 days and 5 day really important? The point of this post is to answer these questions.</p><p>I’ll start by repeating a couple of plots I first made <a href="https://bskiesresearch.wordpress.com/2020/04/20/5-day-doubling-and-the-great-covid-19-uncalibrated-modelling-fiasco/">way back in April 2020</a> when it was just dawning on me what a colossal cock-up SAGE had made of it. These graphs are generated by a simple SEIR model that I’ve shown to reasonably replicate more sophisticated ones. In the below, the blue “calibrated” line uses data up to 14 March to estimate doubling time, which comes out at 3 days. The red “uncalibrated” line uses parameters from Ferguson’s March 16 paper, which has a doubling time of 5 days.</p><figure class="wp-block-image size-large"><a href="https://bskiesresearch.files.wordpress.com/2020/04/performance.png"><img alt="" class="wp-image-1560" data-attachment-id="1560" data-comments-opened="1" data-image-caption="" data-image-description="" data-image-meta="{"aperture":"0","credit":"","camera":"","caption":"","created_timestamp":"0","copyright":"","focal_length":"0","iso":"0","shutter_speed":"0","title":"","orientation":"0"}" data-image-title="performance" data-large-file="https://bskiesresearch.files.wordpress.com/2020/04/performance.png?w=700" data-medium-file="https://bskiesresearch.files.wordpress.com/2020/04/performance.png?w=300" data-orig-file="https://bskiesresearch.files.wordpress.com/2020/04/performance.png" data-orig-size="1400,865" data-permalink="https://bskiesresearch.wordpress.com/2020/04/20/5-day-doubling-and-the-great-covid-19-uncalibrated-modelling-fiasco/performance/" height="395" shrinktofit="true" sizes="(max-width: 1024px) 100vw, 1024px" src="https://bskiesresearch.files.wordpress.com/2020/04/performance.png?w=1024" srcset="https://bskiesresearch.files.wordpress.com/2020/04/performance.png?w=1024 1024w, https://bskiesresearch.files.wordpress.com/2020/04/performance.png?w=150 150w, https://bskiesresearch.files.wordpress.com/2020/04/performance.png?w=300 300w, https://bskiesresearch.files.wordpress.com/2020/04/performance.png?w=768 768w, https://bskiesresearch.files.wordpress.com/2020/04/performance.png 1400w" width="640" /></a></figure><p>So, one obvious point is that the blue curve does a much better job of predicting what was going to happen (ie, the magenta x, which were not used to calibrate either model). But that’s not the point of this particular post. Rather, it’s just that the predictions for 3d vs 5d doubling are radically different. Here is the longer-term view, now without the logarithmic scaling on the axis:</p><figure class="wp-block-image size-large"><a href="https://bskiesresearch.files.wordpress.com/2020/04/forecast.png"><img alt="" class="wp-image-1559" data-attachment-id="1559" data-comments-opened="1" data-image-caption="" data-image-description="" data-image-meta="{"aperture":"0","credit":"","camera":"","caption":"","created_timestamp":"0","copyright":"","focal_length":"0","iso":"0","shutter_speed":"0","title":"","orientation":"0"}" data-image-title="forecast" data-large-file="https://bskiesresearch.files.wordpress.com/2020/04/forecast.png?w=700" data-medium-file="https://bskiesresearch.files.wordpress.com/2020/04/forecast.png?w=300" data-orig-file="https://bskiesresearch.files.wordpress.com/2020/04/forecast.png" data-orig-size="1400,865" data-permalink="https://bskiesresearch.wordpress.com/2020/04/20/5-day-doubling-and-the-great-covid-19-uncalibrated-modelling-fiasco/forecast/" height="395" shrinktofit="true" sizes="(max-width: 1024px) 100vw, 1024px" src="https://bskiesresearch.files.wordpress.com/2020/04/forecast.png?w=1024" srcset="https://bskiesresearch.files.wordpress.com/2020/04/forecast.png?w=1024 1024w, https://bskiesresearch.files.wordpress.com/2020/04/forecast.png?w=150 150w, https://bskiesresearch.files.wordpress.com/2020/04/forecast.png?w=300 300w, https://bskiesresearch.files.wordpress.com/2020/04/forecast.png?w=768 768w, https://bskiesresearch.files.wordpress.com/2020/04/forecast.png 1400w" width="640" /></a></figure><p>Note the “we are here” point is mid-March, when the red and blue curves are visually indistinguishable.</p><p>There are several reasons why the doubling time matters. Firstly, the estimate of <em>current</em> pandemic size is based on <em>historic</em> data. Edmunds <a href="https://bskiesresearch.files.wordpress.com/2023/11/edmunds_evidence.pdf">specifically talks of a 12 day delay</a> from infection to illness, to testing, to finally test data reporting. So 100 cases <em>reported</em>today means 100 infections 12 days ago, and that’s 4 doublings at 3d doubling, meaning 1,600 cases now. If the doubling time was only 5d, then the 12 day delay is just over 2 doublings, and we wouldn’t be at 1,600 cases for another 8 days (4 doublings is 20 days, so that means 12 just past and another 8 in the future). So one immediate consequence of a change in perceived doubling time is that we’ve lost just over a week in terms of pandemic progression. (These calculations all ignore the proportion of infections that are undetected, which can reasonably assume to be roughly constant and thus not affect the argument.) </p><p>Secondly, the 3d doubling means the pandemic comes much sooner, and (thirdly) reaches a much higher peak, as shown in the 2nd graph above. What was expected some time over the summer, is now happening next month, and it’s going to be a lot worse than expected – getting on for twice as many cases per day at peak.</p><p>Finally, the more rapid doubling implies a higher R0-number, and this makes it harder to control. With R0=2.4 (Ferguson’s 16 March number), a reduction of contacts to 40% of normal would control the virus, because 2.4 x 0.4 = 0.96 which is less than 1. Whereas a 3d doubling implies a rather higher R0, let’s say 3.2. This then requires much stiffer action, because 3.2 x 0.4 = 1.28 which is still greater than 1. A reduction to 30% of previous contact levels to get the R number below 1 (3.2 x 0.3 = 0.96 as before) is obviously much tougher to achieve especially given that family members, essential work etc mean we can’t really isolate perfectly. (Quibbling over the exact value of R0 to use doesn’t invalidate the general point that a higher R0 is harder to control.)</p><p>So, changing the estimate of doubling time from 5d to 3d would be a real “oh shit” moment for anyone involved in pandemic planning. It means (a) we’ve instantaneously lost 8 days of lead-time, (b) the pandemic peak is going to be coming a month sooner than expected, (c) the peak is going to be almost twice as big as expected, and (d) the control measures we were hoping to use are much less likely to be adequate. Any plan predicated on a 5d doubling time would immediately have to be revisited in the most extreme and urgent manner.</p><p>I hope I have convinced my reader that whatever plans were in place in early March under the assumption of a 5 day doubling, the new understanding that the doubling time was instead 3d would cause an abrupt and substantial change of perspective. This, from a scientific perspective, is inevitable and obvious.</p></div>James Annanhttp://www.blogger.com/profile/04318741813895533700noreply@blogger.com3tag:blogger.com,1999:blog-9959776.post-79089792726753418582023-11-23T19:32:00.004+00:002023-11-23T19:32:51.541+00:00Vallance vs Vallance vs SAGE: Introduction<p><span style="color: #494949; font-family: Helvetica, sans-serif; font-size: 13px; text-align: justify;">Ok I’m going to do a bit of analysis of Vallance’s evidence to the UK Covid-19 Inquiry, focussing specifically on the events of the mid-March 2020 period up to the imposition of the first “lockdown” on 23rd March. On Monday 20th Nov 2023 he was interviewed by the Inquiry and also provided some written testimony. This is broadly speaking a more detailed version of the testimony he provided back in July 2020 to the House of Commons Science and Technology Committee (which</span><span style="color: #494949; font-family: Helvetica, sans-serif; font-size: 13px; text-align: justify;"> </span><a style="color: #494949; font-family: Helvetica, sans-serif; font-size: 13px; text-align: justify;">I blogged about at the time</a><span style="color: #494949; font-family: Helvetica, sans-serif; font-size: 13px; text-align: justify;">) but appears significantly inconsistent with the documentary evidence provided by the minutes of SAGE meetings and other records of that period. If you already agree with me that Vallance misled the S&TC with his testimony in 2020 then you might not find this very interesting, but I think I might as well go over it again as there’s a lot more testimony to consider (including other participants in SAGE).</span></p><div style="color: #494949; font-family: Helvetica, sans-serif; font-size: 13px; text-align: justify;"><p>I’ll break it up into sections in order to make it digestible, and also to avoid me going round in ever decreasing circles. To start with, let’s consider some background concepts…</p></div>James Annanhttp://www.blogger.com/profile/04318741813895533700noreply@blogger.com0tag:blogger.com,1999:blog-9959776.post-7404655876928592692023-11-21T18:44:00.000+00:002023-11-21T18:44:07.056+00:00 UK Covid-19 Inquiry: Module 2<p><span style="color: #494949; font-family: Helvetica, sans-serif; font-size: 13px; font-weight: bold; text-align: justify;">The currently ongoing Module 2</span><span style="color: #494949; font-family: Helvetica, sans-serif; font-size: 13px; font-weight: bold; text-align: justify;"> </span><a href="https://covid19.public-inquiry.uk/wp-content/uploads/2023/05/Module-2-Outline-of-Scope.pdf" style="font-family: Helvetica, sans-serif; font-size: 13px; font-weight: bold; text-align: justify;">describes its aims thusly:</a></p><div style="color: #494949; font-family: Helvetica, sans-serif; font-size: 13px; text-align: justify;"><p><em>This module will look at, and make recommendations upon, the UK’s core political and administrative decision-making in relation to the Covid-19 pandemic between early January 2020 until February 2022, when the remaining Covid restrictions were lifted. It will pay particular scrutiny to the decisions taken by the Prime Minister and the Cabinet, as advised by the Civil Service, senior political, scientific and medical advisers, and relevant Cabinet sub-committees, between early January and late March 2020, when the first national lockdown was imposed.</em></p><p>I’m particularly interested in this period, as it’s the time that the expert scientific analysis and advice from SAGE was so woefully inadequate. I’ve blogged about this at length, but just to recap, the scientists were mistakenly thinking that the doubling time of the pandemic was about 5-6 days (various numbers appear in the SAGE minutes) and that we shouldn’t take too stringent measures as there was a genuine risk that by doing so we’d put the pandemic off to the following winter when it would add to the normal seasonal pressures on the NHS. They were quite anxious that we should get through it over the summer of 2020 instead.</p><p>Vallance <a href="https://julesandjames.blogspot.com/2020/07/patrick-vallances-faulty-memory.html">misled the Science and Technology Select Committee a while ago about this</a>, claiming that SAGE had recommended lockdown on the 16th or 18th of March. This is contradicted by the minutes of those meetings, and even if you try to argue that the minutes may not be completely definitive on that, it is also contradicted by his accompanying statement that their change of heart was due to correcting their estimate of the doubling time (to 3 days), which the SAGE minutes document very precisely to the 23rd March. He’s due to give evidence to the UK Covid-19 Inquiry on Monday, so I await with interest to see whether he will correct the record or also mislead them.</p><p>This error was not just an inconsequential comment in a committee that no-one cares about, but has been widely reflected in press comment. For example, the usually excellent Lewis Goodall on Xitter:</p><figure class="wp-block-embed is-type-rich is-provider-twitter wp-block-embed-twitter"><div class="wp-block-embed__wrapper"><div class="embed-twitter"><blockquote class="twitter-tweet" data-dnt="true" data-width="550"><p dir="ltr" lang="en">Doesn’t seem to me that what <a href="https://twitter.com/uksciencechief?ref_src=twsrc%5Etfw">@uksciencechief</a> said earlier has received as much attention as it should, in the day’s tsunami of news. In saying that SAGE advised the govt to lockdown a week earlier than they did, yet more space is opening up between them. <a href="https://t.co/cKuWXlh7vH">pic.twitter.com/cKuWXlh7vH</a></p>— Lewis Goodall (@lewis_goodall) <a href="https://twitter.com/lewis_goodall/status/1283830086416859138?ref_src=twsrc%5Etfw">July 16, 2020</a></blockquote></div></div></figure></div>James Annanhttp://www.blogger.com/profile/04318741813895533700noreply@blogger.com1tag:blogger.com,1999:blog-9959776.post-61597301525061452402023-11-20T08:40:00.007+00:002023-11-20T08:40:51.820+00:00UK Covid-19 Inquiry<p> <span style="color: #494949; font-family: Helvetica, sans-serif; font-size: 13px; text-align: justify;">I can see I’m going to have to go over all this again. It’s not a task I really face with much enthusiasm, but it doesn’t seem like anyone else is prepared to do it. To say I’m disappointed at the revisionism, sleight-of-hand and downright misleading testimony from several senior scientists to the UK Covid-19 Inquiry would be an understatement. I had naively hoped there might be some element of humility, introspection and self-reflection concerning their errors at the start of the outbreak, but I’ve seen no hint of this. (If anyone wants to reassure me that lessons have been learnt internally, then I’m all ears, but would want to see evidence of this.)</span></p><div style="color: #494949; font-family: Helvetica, sans-serif; font-size: 13px; text-align: justify;"><p>Unfortunately, neither the inquisitors themselves, nor the journalists following the process, nor the array of commentators eagerly quoting the juicy messages, seem to have the will or perhaps the scientific skills to unpick the story. That’s not to say it is hugely complicated, but a basic understanding of the underlying mathematics is vital for piecing together how it all played out, and why. And it’s very clear that most people start out with an agenda and go looking for support, rather than really being interested in understanding the truth. The scientists are delighted to have found a route to blaming the politicians, and the politicians are too focussed on knifing each other to question what the scientists are now claiming the history to be.</p><p>That’s not to say I’m perfect (far from it), but on this particular topic, I happen to be correct. A more difficult question, is whether anyone else cares. Anyway, on with the show….</p></div>James Annanhttp://www.blogger.com/profile/04318741813895533700noreply@blogger.com0tag:blogger.com,1999:blog-9959776.post-18738389464051858652023-11-19T12:38:00.003+00:002023-11-19T12:38:53.014+00:00 Retired<p><span style="color: #494949; font-family: Helvetica, sans-serif; font-size: 13px; text-align: justify;">As you may have noticed, there hasn’t been a lot of science getting done here recently.</span><span style="color: #494949; font-family: Helvetica, sans-serif; font-size: 13px; text-align: justify;"> </span></p><div style="color: #494949; font-family: Helvetica, sans-serif; font-size: 13px; text-align: justify;"><p class="has-text-align-justify">The basic reason for this is that we’ve decided to retire and close down Blue Skies Research Ltd. We set it up about 10 years ago, when we returned from Japan, and have had a lot of fun continuing our research in a private setting but over the last few years have been gradually winding down the research activity and increasing the other-than-research activity and want to focus on the latter from now on.</p><p>There’s a paper in the works with paper charges still to pay so the company isn’t completely shut down yet. We aren’t looking for new projects but if something exciting comes up, we might change our minds.</p><p>To be honest, we haven’t been particularly inspired by new ideas for a while and simply don’t have any burning climate science questions that we need to answer. After all, we have <a href="https://bskiesresearch.wordpress.com/2020/12/18/science-breakthrough-of-the-year-runner-up/">worked out what Equilibrium Climate Sensitivity is</a> (actually we worked it out in 2006, but everyone else took 15 years to catch up). There are lots of other scientists quite capable of taking the field wherever they choose to, and we look forward to seeing where they go!</p></div>James Annanhttp://www.blogger.com/profile/04318741813895533700noreply@blogger.com1tag:blogger.com,1999:blog-9959776.post-88505052118583075982022-11-18T08:57:00.004+00:002022-11-18T08:57:35.163+00:00No comment necessary<p></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEguAbjQ7w4WHhFPlu-CWQmlbQcWx0lkhGgFB1f2ojFGAh6jomRrlc5ruRcIuu5kvzjJESOg1s_FAzhDcC8lprrnfHgkkvu5EtCSbt5_O7pGRytMk4zSz-fnmO391U_2gPTaE0kmQHNAqh8cSkCsBrFldiDuJZYqd9tG8BBV9-3nr8YsuKI/s914/gdp.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em; text-align: center;"><img border="0" data-original-height="742" data-original-width="914" height="520" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEguAbjQ7w4WHhFPlu-CWQmlbQcWx0lkhGgFB1f2ojFGAh6jomRrlc5ruRcIuu5kvzjJESOg1s_FAzhDcC8lprrnfHgkkvu5EtCSbt5_O7pGRytMk4zSz-fnmO391U_2gPTaE0kmQHNAqh8cSkCsBrFldiDuJZYqd9tG8BBV9-3nr8YsuKI/w640-h520/gdp.png" width="640" /></a></div><div style="text-align: left;"> </div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjrDPIk_EyCmX_x4Npfmq19ECBOpmLUNb9mGH9_-b8SLmDtdgRb3mpYccZcDKfaYT9NxfCXw3_yD8MfHgiuCaOhoSAYqGwTJLBQgvgxDECzeJyEvxeiQ05herwKfR7v3d8Hv6uW_oy917CRGPel7URSlsalJNuk2RkNvlM1bnEQGj0j7Cw/s546/elephant.jpeg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="546" data-original-width="546" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjrDPIk_EyCmX_x4Npfmq19ECBOpmLUNb9mGH9_-b8SLmDtdgRb3mpYccZcDKfaYT9NxfCXw3_yD8MfHgiuCaOhoSAYqGwTJLBQgvgxDECzeJyEvxeiQ05herwKfR7v3d8Hv6uW_oy917CRGPel7URSlsalJNuk2RkNvlM1bnEQGj0j7Cw/w640-h640/elephant.jpeg" width="640" /></a></div><br /><div class="separator" style="clear: both; text-align: center;"><br /></div><br /><p></p>James Annanhttp://www.blogger.com/profile/04318741813895533700noreply@blogger.com0tag:blogger.com,1999:blog-9959776.post-66145515705746160602022-09-21T16:27:00.002+01:002022-09-21T16:28:52.911+01:00Chess<p style="text-align: justify;">Many years ago, I played chess as a schoolboy. Not all that brilliantly, but good enough for the school team which played in various competitions. This fell by the wayside when I went to university, and I'd never had the time or energy to re-start though kept on playing against my uncle when we met. A couple of years ago during covid lockdowns I started playing on-line on chess.com, and then more recently someone started a chess club in Settle where a small bunch of us have been playing fairly informal and quick games. Last weekend was my first proper over-the-board competition, at the very conveniently located <a href="https://www.chesscentre.online/events/festival/d5e7229b-f574-48a1-97af-0e93db241078">Ilkley Chess Festival</a>. I'd naively assumed this would be a local event for local people, but my opponents came from all over, hailing from Portsmouth, Nottingham, Shrewsbury, and even Scarborough. There were also some Scots on the entry list that I didn't meet.</p><p style="text-align: justify;">I've blogged the event on the chess.com site (<a href="https://www.chess.com/blog/jamesthetall/at-ilkla-chess-festival-baht-at-part-1">here</a> and <a href="https://www.chess.com/blog/jamesthetall/at-ilkla-chess-festival-baht-at-part-2">here</a>) as that allows for embedding of games. Spoiler alert: after losing the first game, I won the next 4, ending in 4th place. In the “Intermediate” section, which means under-1750 rated. (I don't have a current rating for OTB chess, so had to guess which section to enter. At school I was about 1450.)</p><p style="text-align: justify;">Someone was taking pictures, so here is a picture of the main hall:</p><p style="text-align: justify;">
<a href="https://brendanogorman.smugmug.com/Chess/2022/Ilkley-Chess-Festival-2022/i-5Xxn8dL/A"><img alt="" src="https://photos.smugmug.com/photos/i-5Xxn8dL/0/L/i-5Xxn8dL-L.jpg" /></a>
<br /></p><p style="text-align: justify;">and here I am, about to win my 3rd game:</p><p style="text-align: justify;"><br /></p><p style="text-align: justify;"><a href="https://brendanogorman.smugmug.com/Chess/2022/Ilkley-Chess-Festival-2022/i-XbvShfM/A"><img alt="" src="https://photos.smugmug.com/photos/i-XbvShfM/0/L/i-XbvShfM-L.jpg" /></a><br /></p><p style="text-align: justify;"><br /></p><p style="text-align: justify;"><br /></p>James Annanhttp://www.blogger.com/profile/04318741813895533700noreply@blogger.com0tag:blogger.com,1999:blog-9959776.post-14062416834805762822022-05-25T07:36:00.006+01:002022-05-30T13:40:22.114+01:00BlueSkiesResearch.org.uk: EGU 2022 – how cold was the LGM (again)?<div style="text-align: justify;">I haven’t blogged in ages but have actually done a bit of work. Specifically, I eventually wrote up my new reconstruction of the Last Glacial Maximum. We did this back in 2012/3 (see <a href="https://julesandjames.blogspot.com/2012/12/how-cold-was-last-glacial-maximum.html">here</a>) but since then there have been lots more model simulations, and then in 2020 Jessica Tierney published a new compilation and analysis of sea surface temperature proxy data. She also produced <a href="https://www.nature.com/articles/s41586-020-2617-x">her own estimate of the LGM temperature anomaly based on this data set</a>, coming up with -6.1±0.4C which seemed both very cold and very precise compared to our own previous estimate of -4.0±0.8C (both ranges at 95% probability).</div><p class="has-text-align-justify" style="text-align: justify;"><span style="font-size: small;">We thought there were quite possibly some problems with her result, but weren’t a priori sure how important a factor this might have been, so that was an extra motivation to revisit our own work.</span></p> <p class="has-text-align-justify" style="text-align: justify;"><span style="font-size: small;">It took a while, mostly because I was trying to incrementally improve our previous method (multivariate pattern scaling) and it took a long time to get round to realising that what I really wanted was an Ensemble Kalman Filter, which is what Tierney et al (TEA) had already used. However, they used an ensemble made by sampling internal variability of a single model (CESM1-2) and a few different sets of boundary conditions (18ka and 21ka for LGM, 0 and 3ka for the pre-industrial), whereas I’m using the PMIP meta-ensemble of PMIP2, PMIP3, and PMIP4 models.</span></p> <p class="has-text-align-justify" style="text-align: justify;">OK, being honest, that was part of the reason, the other part was general procrastination and laziness. Once I could see where it was going, tidying up the details for publication was a bit boring. But it got done, and the paper is <a href="https://cp.copernicus.org/preprints/cp-2022-12/#discussion">currently in review at CPD</a>. Our new headline result is -4.5±1.7C, so slightly colder and much more uncertain than our previous result, but nowhere near as cold as TEA.</p> <p class="has-text-align-justify" style="text-align: justify;"><span style="font-size: small;">I submitted an abstract for the <a href="https://www.egu22.eu/">EGU meeting which is on again right now</a>. It’s fully blended in-person and on-line now, which is a fabulous step forwards that I’ve been agitating for from the sidelines for a while. They used to say it was impossible, but covid forced their hand somewhat with two years of virtual meetings, and now they have worked out how to blend it. A few teething niggles but it’s working pretty well, at least for us as virtual attendees. Talks are very short so rather than go over the whole reconstruction again (I’ve presented early versions previously) I focussed just on one question: why is our result so different from Tierney et al? While I hadn’t set out specifically to critique that work, the reviewers seemed keen to explore, so I’ve recently done a bit more digging into our result. My presentation can be found <a href="https://meetingorganizer.copernicus.org/EGU22/session/42623">via this link, I think</a>.</span></p> <p class="has-text-align-justify" style="text-align: justify;"><span style="font-size: small;">One might assume a major reason might be that the new TEA proxy data set was substantially colder than what went before, but we didn’t find that to be the case. In fact many of the gridded data points coincide physically with the MARGO SST data set which we had previously used, and the average value over these locations was only 0.3C colder in TEA than MARGO (though there was a substantial RMS difference between the points, which is interesting in itself as it suggests that these temperature estimates may still be rather uncertain). A modest cooling of 0.3 in the mean for these SST points might be expected to translate to about 0.5 or so for surface air temperature globally, not close to to the 2.1C difference seen between our 2013 result and their 2020 paper. Also, our results are very similar when we switch between using MARGO and TEA and both together. So, we don’t believe the new TEA data are substantially different from what went before.</span></p> <p style="text-align: justify;"><span style="font-size: small;">What is really different between TEA and our new work is the priors we used. </span></p> <p class="has-text-align-justify" style="text-align: justify;"><span style="font-size: small;">Here is a figure summarising our main analysis, which follows the Ensemble Kalman Filter approach, which means we have a prior ensemble of model simulations (lower blue dots, summarised in the blue gaussian curve above) each of which is updated by nudging towards observations, generating the posterior ensemble of upper red dots and red curve. I’ve highlighted one model in green, which is CESM1-2. Under this plot I have pasted bits of a figure from Tierney et al which shows their prior and posterior 95% ranges. I lined up the scales carefully. You can see that the middle of their ensembles, which are entirely based on CESM1-2, are really quite close to what we get with the CESM1-2 model (the big dots in their ranges are the median of their distributions, which obviously aren’t quite gaussian). Their calculation isn’t identical to what we get with CESM1-2, because it’s a different model simulation, with different forcing, we are using different data and there are various other differences in the details of our calculation. But it’s close.</span></p> <figure class="wp-block-image size-large" style="text-align: justify;"><a href="https://bskiesresearch.files.wordpress.com/2022/05/pic.png"><span style="font-size: small;"><img alt="" class="wp-image-1867" data-attachment-id="1867" data-comments-opened="1" data-image-caption="" data-image-description="" data-image-meta="{"aperture":"0","credit":"","camera":"","caption":"","created_timestamp":"0","copyright":"","focal_length":"0","iso":"0","shutter_speed":"0","title":"","orientation":"0"}" data-image-title="pic" data-large-file="https://bskiesresearch.files.wordpress.com/2022/05/pic.png?w=700" data-medium-file="https://bskiesresearch.files.wordpress.com/2022/05/pic.png?w=300" data-orig-file="https://bskiesresearch.files.wordpress.com/2022/05/pic.png" data-orig-size="1024,768" data-permalink="https://bskiesresearch.wordpress.com/2022/05/24/egu-2022/pic/" height="480" sizes="(max-width: 1024px) 100vw, 1024px" src="https://bskiesresearch.files.wordpress.com/2022/05/pic.png?w=1024" srcset="https://bskiesresearch.files.wordpress.com/2022/05/pic.png 1024w, https://bskiesresearch.files.wordpress.com/2022/05/pic.png?w=150 150w, https://bskiesresearch.files.wordpress.com/2022/05/pic.png?w=300 300w, https://bskiesresearch.files.wordpress.com/2022/05/pic.png?w=768 768w" width="640" /></span></a></figure> <p class="has-text-align-justify" style="text-align: justify;"><span style="font-size: small;">Here is a terrible animated gif. It isn’t that fuzzy in the full presentation. What it shows is the latitudinal temperatures (anomalies relative to pre-industrial) of our posterior ensemble of reconstructions (thin black lines, thick line showing the mean), with the CESM-derived member highlighted in green, and Tierney et al’s mean estimate added in purple. The structural similarity between those two lines is striking. </span></p> <div class="wp-block-image"> <figure class="aligncenter size-large is-resized" style="text-align: justify;"><a href="https://bskiesresearch.files.wordpress.com/2022/05/egu.gif"><span style="font-size: small;"><img alt="" class="wp-image-1863" data-attachment-id="1863" data-comments-opened="1" data-image-caption="" data-image-description="" data-image-meta="{"aperture":"0","credit":"","camera":"","caption":"","created_timestamp":"0","copyright":"","focal_length":"0","iso":"0","shutter_speed":"0","title":"","orientation":"0"}" data-image-title="egu" data-large-file="https://bskiesresearch.files.wordpress.com/2022/05/egu.gif?w=480" data-medium-file="https://bskiesresearch.files.wordpress.com/2022/05/egu.gif?w=300" data-orig-file="https://bskiesresearch.files.wordpress.com/2022/05/egu.gif" data-orig-size="480,360" data-permalink="https://bskiesresearch.wordpress.com/2022/05/24/egu-2022/egu/" height="480" loading="lazy" src="https://bskiesresearch.files.wordpress.com/2022/05/egu.gif?w=480" width="640" /></span></a></figure></div> <p class="has-text-align-justify" style="text-align: justify;"><span style="font-size: small;">A simple calculation also shows that the global temperature field of our CESM-derived sample is closer to their mean in the RMS difference sense, than any other of our ensemble members. Clearly, there’s a strong imprint of the underlying model even after the nudge towards the data sets.</span></p> <p class="has-text-align-justify" style="text-align: justify;"><span style="font-size: small;">So, this is why we think their result is largely down to their choice of prior. While we have a solution that looks like their mean estimate, this lies close to the edge of our range. The reason they don’t have any solutions that look like the bulk of our results is simply that they excluded them <em>a priori</em>. It’s nothing to do with their new data or their analysis method.</span></p> <p class="has-text-align-justify" style="text-align: justify;"><span style="font-size: small;">We’ve been warning against the use of single model ensembles to represent uncertainty in climate change for a full decade now, it’s disappointing that the message doesn’t seem to have got through.</span></p> James Annanhttp://www.blogger.com/profile/04318741813895533700noreply@blogger.com4tag:blogger.com,1999:blog-9959776.post-20919780805103380242022-02-10T16:36:00.000+00:002022-02-10T16:36:01.305+00:00 Marmalade Training Camp<div class="separator" dir="ltr" style="clear: both; text-align: center;">A trip to Scotland last weekend to learn the ancient art of Victorian Marmalade Making from marmalade sensei, the Mother in Law. It turned our to be less art and more chemistry! I still don't quite understand how it worked, but it did. Maybe it is actually magic. It was great weather for the project; continuous rain for 3 days. </div><div class="separator" dir="ltr" style="clear: both; text-align: center;"><br /></div><div class="separator" dir="ltr" style="clear: both; text-align: center;">Step 1. Get Seville oranges, and the same mass of lime and lemons. These kind of oranges are mostly pith and pips, taste very bitter, and can only be found in January, although not only in Scotland. Wash and remove the ends, and any nasty ones.</div><div><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEgZCeyQ1vQPgTPIcy4mQfFnwcbLGZaykxQJjloCVlrylJS6goW0CQ6C_EoEpuhJZtYKWNbIfOq8oZF7G9RrfABLFFuxBDZZIzBvq-uxtWEKQQDn2523-UA-LSutWC_Plz5VAWj0dIfg3ESxiTRClqgJcUZCiJ-UrNE5_v0yuOpAdQ5HPC3Jtnw=s2048" style="display: inline; margin-left: 1em; margin-right: 1em;"> <img border="0" data-original-height="1536" data-original-width="2048" height="164" src="https://blogger.googleusercontent.com/img/a/AVvXsEgZCeyQ1vQPgTPIcy4mQfFnwcbLGZaykxQJjloCVlrylJS6goW0CQ6C_EoEpuhJZtYKWNbIfOq8oZF7G9RrfABLFFuxBDZZIzBvq-uxtWEKQQDn2523-UA-LSutWC_Plz5VAWj0dIfg3ESxiTRClqgJcUZCiJ-UrNE5_v0yuOpAdQ5HPC3Jtnw=w218-h164" width="218" /></a></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEgCojCcjWBjBp4adKtz6teLEhH4As7CnZ4gLBFxP7FhWAu8jYJksvLdMKZ9cXv81cDAExl0bb7JlmGFVenTpmeSlJkonpBKxQ6Xue4a18tDR4T2_BFGs9KVT9_wWAgRsjFn5_3Dmh4BpMBqq6ZXC2cF97tQbCpoVGazGFh2aFjRYy5itCEos60=s2048" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1536" data-original-width="2048" height="163" src="https://blogger.googleusercontent.com/img/a/AVvXsEgCojCcjWBjBp4adKtz6teLEhH4As7CnZ4gLBFxP7FhWAu8jYJksvLdMKZ9cXv81cDAExl0bb7JlmGFVenTpmeSlJkonpBKxQ6Xue4a18tDR4T2_BFGs9KVT9_wWAgRsjFn5_3Dmh4BpMBqq6ZXC2cF97tQbCpoVGazGFh2aFjRYy5itCEos60=w217-h163" width="217" /></a></div><div> <div class="separator" dir="ltr" style="clear: both; text-align: center;">Step 2. Juice fruits! An acceptable diversion from Victorian tradition is to use an electric juicer. The juice goes into the juice pot, the pith and pips into the pith and pits pot, and the shells of rind go to the slicer. The slicer is a large heavy metal thing that clamps to the table, a handle is turned and sliced peel comes out of the bottom. A non-Victorian alternative to the slicer is unknown.</div><div class="separator" dir="ltr" style="clear: both; text-align: center;"><br /></div>
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEjDD0Va_bwOarXDvx31LcwhBtDSlpNGMt8DxBMVv86rQq3H9hQUdz070xxaxmdfe171ANUQ_s3AY3tmDADqG4tA7q1iKX2nssevg8CzCnCkq3nwWo8eGAmHss3Y7e3whI48VTkqVImcw8KooFdOH0WeN4QigzYNal_eLh3gcDIBShkgSLHAYiA=s2048" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="1536" data-original-width="2048" height="188" src="https://blogger.googleusercontent.com/img/a/AVvXsEjDD0Va_bwOarXDvx31LcwhBtDSlpNGMt8DxBMVv86rQq3H9hQUdz070xxaxmdfe171ANUQ_s3AY3tmDADqG4tA7q1iKX2nssevg8CzCnCkq3nwWo8eGAmHss3Y7e3whI48VTkqVImcw8KooFdOH0WeN4QigzYNal_eLh3gcDIBShkgSLHAYiA=w249-h188" width="249" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"></td></tr></tbody></table><br />
</div>
<br />
<br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEiEdeyyGVBbzkM6OmM9qhCY7U8XBlo9aTFd7ix3MLmZ8dgcPM3HF9NRdB9F2dlX88i1xWezyFzu0bykHcUFV3fvcQmyoH8k4oeLDkqHTzNvCBGba9-ISr82Zu3iNBRmuoFsPa3bNNl5Kmv_wpEB-RnjfFFV6wlrhuw2psoBkjEgEC_3Gla7Yoo=s2048" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="2048" data-original-width="1536" height="263" src="https://blogger.googleusercontent.com/img/a/AVvXsEiEdeyyGVBbzkM6OmM9qhCY7U8XBlo9aTFd7ix3MLmZ8dgcPM3HF9NRdB9F2dlX88i1xWezyFzu0bykHcUFV3fvcQmyoH8k4oeLDkqHTzNvCBGba9-ISr82Zu3iNBRmuoFsPa3bNNl5Kmv_wpEB-RnjfFFV6wlrhuw2psoBkjEgEC_3Gla7Yoo=w197-h263" width="197" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"></td></tr></tbody></table><br />
<br />
<div class="separator" dir="ltr" style="clear: both; text-align: center;">Step 3. Add water to the pith and pips bowl and to the rind. pints of water = 1.1 x weight of fruit in lbs, with about 0.1 going into the pith.</div>
<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEiyAWzxx8sQ2ImxL10j2UnlrefwhfkXPADBJTzXNY87R0jyfixv2QA_oqj19-LVIfhbv4zK4lE31pXpvkS0epTAJviu49MblCUqAsmnsjeGlwkt9Vl6DmQC3WCZ9xVhf6gxcbu-FdwKEesM3rcDrP1FDVYBOtLTEkrfLlpP-sa8XlHCHrNzlWk=s2048" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="2048" data-original-width="1536" height="241" src="https://blogger.googleusercontent.com/img/a/AVvXsEiyAWzxx8sQ2ImxL10j2UnlrefwhfkXPADBJTzXNY87R0jyfixv2QA_oqj19-LVIfhbv4zK4lE31pXpvkS0epTAJviu49MblCUqAsmnsjeGlwkt9Vl6DmQC3WCZ9xVhf6gxcbu-FdwKEesM3rcDrP1FDVYBOtLTEkrfLlpP-sa8XlHCHrNzlWk=w181-h241" width="181" /></a></div>
<div class="separator" dir="ltr" style="clear: both; text-align: center;"><br /></div><div class="separator" dir="ltr" style="clear: both; text-align: center;">Step 4. Soaking the fruit is neither here not there as far as the chemistry/magic is concerned, apparently. But by now you will be tired, so you can take a break ... overnight if you like.</div><div class="separator" dir="ltr" style="clear: both; text-align: center;"><br /></div>
<table cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEipDNGZBEwPTgG5NqnsK0gQrDDH4squ16ITXlIakO8w9PMLjmkZO8kBvUpzGMd_AmRebDKJKSSqc0AHf92Bb2RafRUvdCUza6aEdc2TDP8Kyaua6jcFRTVIVBQkHD6lijDIOG-Z4KgIJ32JRpe1i-16_zU-uAGYrxCopwcF2BpiB4t4iKgDfjg=s2048" style="clear: left; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" data-original-height="1536" data-original-width="2048" height="207" src="https://blogger.googleusercontent.com/img/a/AVvXsEipDNGZBEwPTgG5NqnsK0gQrDDH4squ16ITXlIakO8w9PMLjmkZO8kBvUpzGMd_AmRebDKJKSSqc0AHf92Bb2RafRUvdCUza6aEdc2TDP8Kyaua6jcFRTVIVBQkHD6lijDIOG-Z4KgIJ32JRpe1i-16_zU-uAGYrxCopwcF2BpiB4t4iKgDfjg=w275-h207" width="275" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Don't forget your cat!</td></tr></tbody></table><div class="separator" style="clear: both; text-align: center;">
<div class="separator" dir="ltr" style="clear: both; text-align: center;"><br /></div><div class="separator" dir="ltr" style="clear: both; text-align: center;">Step 5. Find cauldron! Put rind-marinade into cauldron.</div><div class="separator" dir="ltr" style="clear: both; text-align: center;"><br /></div>
<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEizeVZEUdZPNYF4puaVmFGmOcJ8aRZ62d_qdCRDg7bk97jKwQsKdOMpX7kHsfcxA2whsuYQ08q4i2g1nWaifkT6yaA_Hq1a6IKc3mC0rics6STP1q-UdjkdGUaGMoHt8w_o1QbCvocws075CVy4TSIhEzOU-IfOIuO97PFc8VeoCJKk34-2nc0=s2048" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="2048" data-original-width="1536" height="265" src="https://blogger.googleusercontent.com/img/a/AVvXsEizeVZEUdZPNYF4puaVmFGmOcJ8aRZ62d_qdCRDg7bk97jKwQsKdOMpX7kHsfcxA2whsuYQ08q4i2g1nWaifkT6yaA_Hq1a6IKc3mC0rics6STP1q-UdjkdGUaGMoHt8w_o1QbCvocws075CVy4TSIhEzOU-IfOIuO97PFc8VeoCJKk34-2nc0=w199-h265" width="199" /></a>
<div class="separator" dir="ltr" style="clear: both; text-align: center;"><br /></div><div class="separator" dir="ltr" style="clear: both; text-align: center;">Step 6. Manufacture a bag from cloth and string that contains the pith and pips, and suspend in cauldron. This bag contains the magical carbohydrate pectin which is required to make the marmalade set. Bring to boil and cook for an hour (the internet suggests 2-3 hours for bright, tender marmalade. The internet might be wrong.). Apparently the acid from the fruit helps get the pectin out, but I don't understand this, becuase the juice is not yet added at this stage. </div>
<a href="https://blogger.googleusercontent.com/img/a/AVvXsEiThU5xY19p8ReOPhVjVMwCw_HK6lgaqJLkSBLLVWZCiJkOTubOkqBHMMdv-n-Utw-haUcVx-6m_qpbRd-VxxFVMXDjlpfm3Tll709_vHXoYiYqHcSLonKgYetWNXQz2HaeXwHTDEWP29vrEif0YOs1GKqDXtjUgtEGySHyIr4nfh97kjFL1do=s2048" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="2048" data-original-width="1536" height="272" src="https://blogger.googleusercontent.com/img/a/AVvXsEiThU5xY19p8ReOPhVjVMwCw_HK6lgaqJLkSBLLVWZCiJkOTubOkqBHMMdv-n-Utw-haUcVx-6m_qpbRd-VxxFVMXDjlpfm3Tll709_vHXoYiYqHcSLonKgYetWNXQz2HaeXwHTDEWP29vrEif0YOs1GKqDXtjUgtEGySHyIr4nfh97kjFL1do=w204-h272" width="204" /></a>
<div class="separator" dir="ltr" style="clear: both; text-align: center;"><br /></div><div class="separator" dir="ltr" style="clear: both; text-align: center;">Step 7. Turn off the heat. Extract bag from cauldron and squeeze it hard to get out all the pectin. </div>
<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEg6HuendGYJC9gdgB2UOB26glVJI8MlM2ONTNBjRDJUUJ2_yGl-B5Byj782RFINFODRMWpwSWn71_Zt8m-n-6eh-qI6XRl2PxHu49IYcOTYh216KFjikmVeZNp2dDd-8g9C0sBh6Mz0P9HlmarIOvMzAeuOSuhtnZsqYUh9PdCZfEAoM-hdN78=s2048" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="2048" data-original-width="1536" height="263" src="https://blogger.googleusercontent.com/img/a/AVvXsEg6HuendGYJC9gdgB2UOB26glVJI8MlM2ONTNBjRDJUUJ2_yGl-B5Byj782RFINFODRMWpwSWn71_Zt8m-n-6eh-qI6XRl2PxHu49IYcOTYh216KFjikmVeZNp2dDd-8g9C0sBh6Mz0P9HlmarIOvMzAeuOSuhtnZsqYUh9PdCZfEAoM-hdN78=w197-h263" width="197" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div>Step 8. Add juice.<br /><div class="separator" style="clear: both; text-align: center;"><br /></div><div style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEgbAHTAo0knxUQPHMRQjkXC2YUnGkTa8A9blxc0TXYeuDTDaoceEoS2cx-vnlqkduzXIUDQQssJMx8veDeldsyLP2gPVPRuZaQVT5wGPK-6q5VEJt_qAYI92VibgLvuHdlp3eGZoSlHscvb2-IHSvHq5HEFHq0GvhTYpPxEhFxhxwcHrPhT3f4=s2048" style="clear: left; margin-bottom: 1em;"><img border="0" data-original-height="2048" data-original-width="1536" height="280" src="https://blogger.googleusercontent.com/img/a/AVvXsEgbAHTAo0knxUQPHMRQjkXC2YUnGkTa8A9blxc0TXYeuDTDaoceEoS2cx-vnlqkduzXIUDQQssJMx8veDeldsyLP2gPVPRuZaQVT5wGPK-6q5VEJt_qAYI92VibgLvuHdlp3eGZoSlHscvb2-IHSvHq5HEFHq0GvhTYpPxEhFxhxwcHrPhT3f4=w210-h280" width="210" /></a></div><div class="separator" style="clear: both; text-align: center;">
<div class="separator" dir="ltr" style="clear: both; text-align: center;"><br /></div>
<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEgbAHTAo0knxUQPHMRQjkXC2YUnGkTa8A9blxc0TXYeuDTDaoceEoS2cx-vnlqkduzXIUDQQssJMx8veDeldsyLP2gPVPRuZaQVT5wGPK-6q5VEJt_qAYI92VibgLvuHdlp3eGZoSlHscvb2-IHSvHq5HEFHq0GvhTYpPxEhFxhxwcHrPhT3f4=s2048" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"></a>
<div class="separator" dir="ltr" style="clear: both; text-align: center;">Step 9. Add sugar</div>
<a href="https://blogger.googleusercontent.com/img/a/AVvXsEilLFPhyUNsdPAjUWIVr62_jj5tZoG5ZtEa3DjPUV63L7MXDEg1IFwz6n6CPJWqyRQGU1oUmf8HX9GRZPFIk2bmRJ2-9ONwWMQS3X-5Fpt2a5o2mo5bzdRzGBQM-sUJZ26q16Y4hLFPdWDBMrsGKO_sUQT9f1eyRXkXjk5UnH01kzwd_Ikkevc=s2048" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="2048" data-original-width="1536" height="278" src="https://blogger.googleusercontent.com/img/a/AVvXsEilLFPhyUNsdPAjUWIVr62_jj5tZoG5ZtEa3DjPUV63L7MXDEg1IFwz6n6CPJWqyRQGU1oUmf8HX9GRZPFIk2bmRJ2-9ONwWMQS3X-5Fpt2a5o2mo5bzdRzGBQM-sUJZ26q16Y4hLFPdWDBMrsGKO_sUQT9f1eyRXkXjk5UnH01kzwd_Ikkevc=w209-h278" width="209" /></a></div></div></div><br /><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;">
<div class="separator" style="clear: both; text-align: center;">Step 10. Add more sugar </div>
<a href="https://blogger.googleusercontent.com/img/a/AVvXsEhRoSckalQZrAKCESgznmCBcGs_hbZigLWxp0ho0Jf2zhhEf_wopbJV2hzXmY30Au-z5GLb715l42-u76gDNwkpjEAt6nKBBetE1tz1DS2SNoViI0W11rr9S1fYh2wHzGIcrjt4zYnR7V7OVnOqi2UU6hgX3baOS8XH46Js4jcs32lJNAo0Gyc=s2048" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="2048" data-original-width="1536" height="286" src="https://blogger.googleusercontent.com/img/a/AVvXsEhRoSckalQZrAKCESgznmCBcGs_hbZigLWxp0ho0Jf2zhhEf_wopbJV2hzXmY30Au-z5GLb715l42-u76gDNwkpjEAt6nKBBetE1tz1DS2SNoViI0W11rr9S1fYh2wHzGIcrjt4zYnR7V7OVnOqi2UU6hgX3baOS8XH46Js4jcs32lJNAo0Gyc=w215-h286" width="215" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div>
<div class="separator" dir="ltr" style="clear: both; text-align: center;">Steps 11-13. Add yet more sugar. About 1.6x weight of fruit in total!!!! </div><div class="separator" dir="ltr" style="clear: both; text-align: center;"><br /></div><div class="separator" dir="ltr" style="clear: both; text-align: center;">Step 14. Bring slowly to a rolling boil. </div>
<a href="https://blogger.googleusercontent.com/img/a/AVvXsEiaK_DOvbBvp48tftH3U7e0fc9rzY0abFwB1O0rRI-7qKTG7-O4r8zZ7vPsSHIlNerG8cCAkf3tUWRvtnv6HLaiddR-vO98NRGhkLTRWYWLBlXPLIfARiha3xAgeG_hwjSpN2tRKV9eUsddxgPN3-YhYnZIdLKYmaCRcwyGaCNqBkmLy91zG5g=s2048" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="2048" data-original-width="1536" height="277" src="https://blogger.googleusercontent.com/img/a/AVvXsEiaK_DOvbBvp48tftH3U7e0fc9rzY0abFwB1O0rRI-7qKTG7-O4r8zZ7vPsSHIlNerG8cCAkf3tUWRvtnv6HLaiddR-vO98NRGhkLTRWYWLBlXPLIfARiha3xAgeG_hwjSpN2tRKV9eUsddxgPN3-YhYnZIdLKYmaCRcwyGaCNqBkmLy91zG5g=w208-h277" width="208" /></a>
<a href="https://blogger.googleusercontent.com/img/a/AVvXsEhXWNmJmjhOw5HvrQW2mgFXtQP_yuPZXfCT6QwDQKcX5GVW1poqZGqX9hRPOq73-uWR-TfTc-ngYnAosRFY2hsQ4EAJDdT8lReIe79TTnPDXi-7hLWtvM0DSeR4HVstyQPvXZ6JXbQSEWQbugeNxlahvp08ZhJWUX6peiecsWkmSLVR3BvsNuE=s2048" style="margin-left: 1em; margin-right: 1em;"></a><img a="" border="0" data-original-height="2048" data-original-width="1536" height="279" src="https://blogger.googleusercontent.com/img/a/AVvXsEhXWNmJmjhOw5HvrQW2mgFXtQP_yuPZXfCT6QwDQKcX5GVW1poqZGqX9hRPOq73-uWR-TfTc-ngYnAosRFY2hsQ4EAJDdT8lReIe79TTnPDXi-7hLWtvM0DSeR4HVstyQPvXZ6JXbQSEWQbugeNxlahvp08ZhJWUX6peiecsWkmSLVR3BvsNuE=w209-h279" width="209" /> <br /><br /><br />Step 15. Excitedly test every 5 seconds to see if it is done yet. It is done when it sets. This is the magic/chemistry bit. Pectin and acid and heated up sugar and do something or other that makes - jelly. But this isn't the same as caramalisation that you use to make toffee, which is more like burning sugar. In fact you want as little caramalisation as possible, because marmalade shouldn't taste like toffee. This is why the internet says boil for 15-20mins. The internet also says too much boiling at this stage make the rind tough. It was more like an hour for us, but our marmalade is still pretty and the rind very nice. Maybe internet people want the rind to melt in their mouths or something weird?</div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;">Anyway, you can test by cooling a small spoonful on a plate and when it starts to set it is done, or use a Victorian thermometer. Not sure what the markings on the thermometer engraved by ancestors mean, but when the brass holder gets all sticky with globs of marmalade, it is done.<br /><br />
</div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEgpKVWmivt4PhAo-zojrTZwXH_1DVvtvYMEYLqquZVQTG-EG4LgxpuwFrGTTK3C4gKOt-rkXBmtx54gVTVXI4ZvRDnc61LGubju9vdtGELRvkw5QGuX-w3MPM_ctVFkQGcUxHYckbXs10nYMYBiu5gLR-8QMvIU95jrZzqey7ojXpwQSe1Zgt0=s2048" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="2048" data-original-width="1536" height="260" src="https://blogger.googleusercontent.com/img/a/AVvXsEgpKVWmivt4PhAo-zojrTZwXH_1DVvtvYMEYLqquZVQTG-EG4LgxpuwFrGTTK3C4gKOt-rkXBmtx54gVTVXI4ZvRDnc61LGubju9vdtGELRvkw5QGuX-w3MPM_ctVFkQGcUxHYckbXs10nYMYBiu5gLR-8QMvIU95jrZzqey7ojXpwQSe1Zgt0=w195-h260" width="195" /></a></div><br />Step 16. Remove from heat and quickly fill up all your jars (which, hopefully, appear beside you by magic) and screw the lids on ASAP. </div><div class="separator" style="clear: both; text-align: center;"><br /><div class="separator" style="clear: both; text-align: center;"> <a href="https://blogger.googleusercontent.com/img/a/AVvXsEio9JsG4pRLQUJgUWQhq-5oJC8J3Ri26YeXoYI8WLKxYBZf4sriHybQsM-GUnvjmedBRr15WsMF5nMCe8b-lOPPgc_W1-2G2pGvNM6VFJf42t-INlNC1-BAwYAL41blREXtbCf2nlU64m_WFQx4ZvkGZ6K-qtqzDC3kSm1payeBewg3mDAuXd4=s2048" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="2048" data-original-width="1536" height="287" src="https://blogger.googleusercontent.com/img/a/AVvXsEio9JsG4pRLQUJgUWQhq-5oJC8J3Ri26YeXoYI8WLKxYBZf4sriHybQsM-GUnvjmedBRr15WsMF5nMCe8b-lOPPgc_W1-2G2pGvNM6VFJf42t-INlNC1-BAwYAL41blREXtbCf2nlU64m_WFQx4ZvkGZ6K-qtqzDC3kSm1payeBewg3mDAuXd4=w215-h287" width="215" /></a></div><br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEgFdaw1MDL423tyIFjCcMlX7TyES0iyE9aJDIAvWNNMp-VKzrGvxTtt7ePlny-55ksogc2PsPWGcsSHtwGXT1PfBdThXGB6nc-0VqDZ9VVwquW4PHKDTY7wMojeK4uG8szaUrhcHFkfykq4wvgsuGlLosVDdcKPY7DacyW0llvz4vIFdQXh6xk=s2048" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1536" data-original-width="2048" height="333" src="https://blogger.googleusercontent.com/img/a/AVvXsEgFdaw1MDL423tyIFjCcMlX7TyES0iyE9aJDIAvWNNMp-VKzrGvxTtt7ePlny-55ksogc2PsPWGcsSHtwGXT1PfBdThXGB6nc-0VqDZ9VVwquW4PHKDTY7wMojeK4uG8szaUrhcHFkfykq4wvgsuGlLosVDdcKPY7DacyW0llvz4vIFdQXh6xk=w444-h333" width="444" /></a></div><br /><br />Optional Step. Next day, if some of your jars are not screw top, or they are screw top but the button on the lid didn't go down as the marmalade cooled, or you don't have lids... melt paraffin wax (in a jug in boiling water) and pour over the top and slap on some kind of lid! Marmalade will stay good for ... 3 years or so?<br /><br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEjqtQGOT3MsMHx8xpv8aMvU5c3PP7ENbJGDdyQF0-vFC3QvBMFsS2mgWNrcU1rJJ_32ZQ6xGNWwN-hKJTvxD6gcmnTp3yAGMRY33RzBk23t6Q0Jf9D7MR71cEdPFFYnsCo7bkPl1HGoCedekx9_etn0eigwAxHu0t0M3QwIncQuhTXUtX-e74s=s2048" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1536" data-original-width="2048" height="151" src="https://blogger.googleusercontent.com/img/a/AVvXsEjqtQGOT3MsMHx8xpv8aMvU5c3PP7ENbJGDdyQF0-vFC3QvBMFsS2mgWNrcU1rJJ_32ZQ6xGNWwN-hKJTvxD6gcmnTp3yAGMRY33RzBk23t6Q0Jf9D7MR71cEdPFFYnsCo7bkPl1HGoCedekx9_etn0eigwAxHu0t0M3QwIncQuhTXUtX-e74s=w202-h151" width="202" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEhCT2RmxURkVsRWJiHRaw9NHB_BaXE_UgUBD8VH84Dmda5gOFS9o5ip6FksYXFaVoZDVP2OvBmz8PVhaKenmGV0Vtlj1yNJbCpI_nE_VdNDtzPUA81HoIzKQ8T_8qvi6uRjhTqcVmR82yVQ6jHJv_aucY-ktUKqJYGYEdmYr-59dpgJaropRR8=s2048" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1536" data-original-width="2048" height="240" src="https://blogger.googleusercontent.com/img/a/AVvXsEhCT2RmxURkVsRWJiHRaw9NHB_BaXE_UgUBD8VH84Dmda5gOFS9o5ip6FksYXFaVoZDVP2OvBmz8PVhaKenmGV0Vtlj1yNJbCpI_nE_VdNDtzPUA81HoIzKQ8T_8qvi6uRjhTqcVmR82yVQ6jHJv_aucY-ktUKqJYGYEdmYr-59dpgJaropRR8=s320" width="320" /></a></div><br /><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;">Step 17. Eat. Yum yum!</div> <p></p></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEidmzeXOV3Sp1Mrv_wFwjMWoTU0C8NV8m19QUqc_KMeYAeXPymIRbMe6bnQXGimffEqgYKZZ6AaFRXnlz5nFRdC8jMd52_DACEFkqz94ADGkvSHzwfQC-nY3erUpG_9ZotRpXlap8h-VSGW23tlMJQ0_b0H8zCFMNsvol884NJCGH1SvdhAgwU=s2048" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="2048" data-original-width="1536" height="320" src="https://blogger.googleusercontent.com/img/a/AVvXsEidmzeXOV3Sp1Mrv_wFwjMWoTU0C8NV8m19QUqc_KMeYAeXPymIRbMe6bnQXGimffEqgYKZZ6AaFRXnlz5nFRdC8jMd52_DACEFkqz94ADGkvSHzwfQC-nY3erUpG_9ZotRpXlap8h-VSGW23tlMJQ0_b0H8zCFMNsvol884NJCGH1SvdhAgwU=s320" width="240" /></a></div><br />juleshttp://www.blogger.com/profile/02591920483149775255noreply@blogger.com1tag:blogger.com,1999:blog-9959776.post-39081363689436315982021-12-19T17:06:00.005+00:002021-12-19T17:19:45.982+00:00Omicron<p style="text-align: justify;">It occurred to me that the talk of perhaps bringing in restrictions some time in the future was probably poorly timed, in that we are probably pretty close to the peak right now and if action is going to be worthwhile, it needs to be pretty much immediate. Having made a few comments to that end on twitter, I thought I should check out my intuition with some calculations. So here they are.</p><p style="text-align: justify;">My starting point is that the Omicron variant represented 22% of tests on the 11th Dec (<a href="https://twitter.com/AlastairGrant4/status/1470865942993330179?s=20">link</a>) and we had about 40k positive tests on that day (<a href="https://coronavirus.data.gov.uk/details/cases">link</a> - but see additional note at bottom of post) meaning 9k tested cases which I will assume represents 18k real infections (ie 50% of infections are actually observed) and furthermore I'll assume that these infections happened on the 8th as it must take a little while to feel ill and get tested. </p><p style="text-align: justify;">I'm using a doubling time of about 2 days with an underlying R0 number of 6, and another assumption I'm making is that the population is about 50% immune. I'm ignoring the Delta infection which is small in comparison and carries on largely in parallel with Omicron.</p><p style="text-align: justify;">So I initialise the model to hit 18k infections on the 8th, and ran it forwards. This is what I get with no action at all, just the natural infection profile of an uncontrolled epidemic:</p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEibQEYx0bBMWKzL84QnLL4Ds96GLshRBfMWGidDx3f4EUoJKT1TFzGUknWNrqO-T3R-19zoXD5ebUfFAB-YjFbXCIf1d3WRs1S83a4d_4qjnHF1irIQhe7OU0azGqwkWXTOYHESjKN0ivAyxuv2coyH77oV4gQks3g_s6tTEf1TvqwYdL8=s1116" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="689" data-original-width="1116" height="396" src="https://blogger.googleusercontent.com/img/a/AVvXsEibQEYx0bBMWKzL84QnLL4Ds96GLshRBfMWGidDx3f4EUoJKT1TFzGUknWNrqO-T3R-19zoXD5ebUfFAB-YjFbXCIf1d3WRs1S83a4d_4qjnHF1irIQhe7OU0azGqwkWXTOYHESjKN0ivAyxuv2coyH77oV4gQks3g_s6tTEf1TvqwYdL8=w640-h396" width="640" /></a></div><div class="separator" style="clear: both; text-align: justify;">32 million infections in total, with a daily peak of 2.7 million on the 27th.</div><div class="separator" style="clear: both; text-align: justify;"><br /></div><div class="separator" style="clear: both; text-align: justify;">If instead we were to introduce severe restrictions now, such that the underlying R0 dropped from 6 to 1.5, the epidemic would be much smaller:</div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEgG5bx_26NYMP5I5wJLsMP8BA_-P907MtCxzggtB_DuT2pT19ELxvCXYOD08X7Os0WoRGcWkGXTEHfTvceSl53H-iaMRtV8JkqPCDj18gWzSdCg_tNqszyWOLZqXGLKM-q34VsuEKd6dt9YPh6x6DGbnr1sAnC-O07DQbydkZLfQWSZQBg=s1116" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="689" data-original-width="1116" height="396" src="https://blogger.googleusercontent.com/img/a/AVvXsEgG5bx_26NYMP5I5wJLsMP8BA_-P907MtCxzggtB_DuT2pT19ELxvCXYOD08X7Os0WoRGcWkGXTEHfTvceSl53H-iaMRtV8JkqPCDj18gWzSdCg_tNqszyWOLZqXGLKM-q34VsuEKd6dt9YPh6x6DGbnr1sAnC-O07DQbydkZLfQWSZQBg=w640-h396" width="640" /></a></div>A daily max of about 430k infections and only 4 million in total. Note that the underlying R0 dropping to 1.5 means the effective R value drops to about 0.75 as the population is half immune.<div><br /></div><div>However the Govt seems to be slowly meandering towards the possibility of some restrictions in about a week. If we were to say Boxing Day instead, then we get:<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEhguazAkOk0zfCFSq0lCeDrkEJUyjvLIe4IWMqypaNKPgSvO5JiqC_kpjuxRwxDNQMyx9Ljuoow_1YJCbHABY_wg5TDVu5h7w4GgFAFR0bXhSNCjq-AMHKlk7KV0P51thHLChGCXszt77L13KfZxZQNTe6e_Xd8F5TOiNpNSjvrk6RF8OU=s1116" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="689" data-original-width="1116" height="396" src="https://blogger.googleusercontent.com/img/a/AVvXsEhguazAkOk0zfCFSq0lCeDrkEJUyjvLIe4IWMqypaNKPgSvO5JiqC_kpjuxRwxDNQMyx9Ljuoow_1YJCbHABY_wg5TDVu5h7w4GgFAFR0bXhSNCjq-AMHKlk7KV0P51thHLChGCXszt77L13KfZxZQNTe6e_Xd8F5TOiNpNSjvrk6RF8OU=w640-h396" width="640" /></a></div><br /><div class="separator" style="clear: both; text-align: center;"><span style="text-align: justify;"><br /><div style="text-align: justify;">The daily max here is 2.4 million, with the total about 16 million. So even this delayed action does cut the epidemic in half, by shutting it down rapidly from the peak. That's a bit better than my intuition had suggested to me.</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">The details of these calculations are sensitive to the timing of the peak of course, which depends on all the assumptions I've made. What is not in doubt is that every day makes quite a big difference to the outcome.</div></span></div><div class="separator" style="clear: both; text-align: justify;"><br /></div></div><div class="separator" style="clear: both; text-align: justify;">Edit: In the time it took me to write this post, the number of cases by specimen date on the 11th has been updated to 46k!</div>James Annanhttp://www.blogger.com/profile/04318741813895533700noreply@blogger.com4tag:blogger.com,1999:blog-9959776.post-84129762114071743982021-10-16T14:26:00.002+01:002021-10-16T14:26:12.328+01:00More COVID<p style="text-align: justify;">Posting this mostly because some people seem to be under the misapprehension that the UK is doing really well at coping with COVID, at least in comparison to our European neighbours. It's simply not true, though it's hard to discern quite how poorly we are doing from most of the media including the BBC. <a href="https://www.ft.com/content/34582534-4510-4d45-bcba-2f9e04005309">This article in the FT</a> presents some of the data, and I'll take some more from <a href="https://ourworldindata.org/coronavirus">OWID</a>.</p><p style="text-align: justify;">While the rapid start of the vaccination campaign was certainly impressive and genuinely superior to the rest of the EU, we have now been overtaken by many of our neighbours.</p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi5PNgyvAFHF7y9Itn7vq5NZF8q-iEPf_aiijO0DZDniyja95CPCUh5b-Y0fbrV8Yp3RmQLfWha3ByADLpzhgnUGqMRvNT35zC-QK6acbHtCpc9BqY7_3icw8u5_LNvhe3bZWc/s2048/Screenshot+2021-10-16+at+13.44.34.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1179" data-original-width="2048" height="368" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi5PNgyvAFHF7y9Itn7vq5NZF8q-iEPf_aiijO0DZDniyja95CPCUh5b-Y0fbrV8Yp3RmQLfWha3ByADLpzhgnUGqMRvNT35zC-QK6acbHtCpc9BqY7_3icw8u5_LNvhe3bZWc/w640-h368/Screenshot+2021-10-16+at+13.44.34.png" width="640" /></a></div><div style="text-align: justify;"><br /></div><p style="text-align: justify;">That's us 2nd from bottom on that chart of major European nations.</p><p style="text-align: justify;">Vaccination of children has been abysmal, both with the stupid delay due to JCVI's shilly-shallying, and then the slow roll-out. Boosters are running at about half the rate that the original vaccination was, so the backlog is growing rapidly.</p><p style="text-align: justify;"> </p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhZK2T7zaX4ssu2US5-THzDAoxhDMi9LeeJXLFnsPeAA0WJDjysSZmBe6aMoKJkx8vQbUpeEyQre5KIk1PoF9DvNAVyR-G1CwtJtivTSKG1hyphenhyphenIoo6Bqnxe06cTe6liABVi6rCA/s1440/Screenshot+2021-10-16+at+13.27.01.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="876" data-original-width="1440" height="390" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhZK2T7zaX4ssu2US5-THzDAoxhDMi9LeeJXLFnsPeAA0WJDjysSZmBe6aMoKJkx8vQbUpeEyQre5KIk1PoF9DvNAVyR-G1CwtJtivTSKG1hyphenhyphenIoo6Bqnxe06cTe6liABVi6rCA/w640-h390/Screenshot+2021-10-16+at+13.27.01.png" width="640" /></a></div><br /><p style="text-align: justify;">Our own volunteer-run vacc centre was mothballed a while back, we could be doing a thousand a day no problem, but it's apparently not part of the plan.</p><p style="text-align: justify;">Case numbers are far higher here than just about anywhere else in Europe. USA is comparable, which is hardly an endorsement.</p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjv-VP4ygSu0_qO6X-0FCZgIHfqWW3T6k18l6PwNlQJiyYCMTK7DRZzM6jSpyGWIPCSVIX8FdXi-XDYEN6dMp08KSmPB21VTMq5acNw0K9p3DuP7tYKtIVCUTgZCKQCjxgW4cw/s1902/Screenshot+2021-10-16+at+13.40.58.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1072" data-original-width="1902" height="360" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjv-VP4ygSu0_qO6X-0FCZgIHfqWW3T6k18l6PwNlQJiyYCMTK7DRZzM6jSpyGWIPCSVIX8FdXi-XDYEN6dMp08KSmPB21VTMq5acNw0K9p3DuP7tYKtIVCUTgZCKQCjxgW4cw/w640-h360/Screenshot+2021-10-16+at+13.40.58.png" width="640" /></a></div><br /><div class="separator" style="clear: both; text-align: justify;"><br /></div><div class="separator" style="clear: both; text-align: justify;">And of course plenty of deaths too:</div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg-3iszi1stN60eDKgn9EmYI0q-hVZg424Pd_rFDQc1UAUFZvx-IdKf_HNl5vDThMSDfAJlzi5kUPYmdeJtgC6Nq-tHRgsh8sigKosrJE1yBr6IdXPM7TN1xFrA3ViYRis1fd4/s1912/Screenshot+2021-10-16+at+13.41.35.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1084" data-original-width="1912" height="362" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg-3iszi1stN60eDKgn9EmYI0q-hVZg424Pd_rFDQc1UAUFZvx-IdKf_HNl5vDThMSDfAJlzi5kUPYmdeJtgC6Nq-tHRgsh8sigKosrJE1yBr6IdXPM7TN1xFrA3ViYRis1fd4/w640-h362/Screenshot+2021-10-16+at+13.41.35.png" width="640" /></a></div><br /><p style="text-align: justify;">Yes, both France and Spain had a bit of bump in the late summer, but quickly got on top of it, which we haven't bothered to do. There's no sign of any improvement and in fact the recent case numbers are ticking up quite firmly, so we can probably expect deaths to follow. The deaths aren't really the only problem of course, the knock-on effect of pressure on the hospitals affects a much broader range of people who aren't even infected.</p><p style="text-align: justify;">In case you are thinking optimistically that just about everyone must have had it by now and the numbers must be about to go down, I've seen it said that some regions of Iraq, the total number of cases to date is substantially higher than the population, i.e. many people have had it twice or more. Immunity doesn't last. Of course the severity of the disease is far lower after vaccination, and hopefully will also drop with prior infection. But it's not going to go away and the reluctance of the govt to take any action to help control the disease probably means we'll be stuck with very high levels for the foreseeable future.</p>James Annanhttp://www.blogger.com/profile/04318741813895533700noreply@blogger.com4tag:blogger.com,1999:blog-9959776.post-15552098850009352502021-04-14T21:35:00.009+01:002021-04-16T15:09:21.242+01:00Speed vs power in Zwift<p style="text-align: justify;">This may be of interest to a relatively small number of readers, but it seems worth documenting that the relationship between power and equilibrium flat speed in the cycling simulator <a href="https://www.zwift.com/">Zwift</a> can be quite accurately summarised via </p><p style="text-align: justify;">P = 1.86e-02 w.v - 5.37e-04 v^3 + 2.23e-05 w.v^3 + 1.33e-05 h.v^3</p><p style="text-align: justify;">where v is the velocity in kph, w is the rider weight in kg, and h is the rider height in cm.</p><p style="text-align: justify;">The linear term in v can be thought of as arising through rolling resistance (which also varies with w), with the three cubic terms due to air resistance. These cubic terms can be thought of as the dominant terms in a Taylor series expansion of a single term that looks like A.f(w,h).v^3 where f is a function of weight and height that modifies the resistance (eg though changing the cross sectional area). At first I was trying to work out what f was, but an important realisation that only came to me while doing this analysis is that I don't actually need to know its form as the values of w and h only deviate moderately from their mean values for the practical range of riders I'm interested in (ie ± 10% the most part, 20% at worst). Therefore this linearisation approach (with coefficients fitted through linear regression) is plenty good enough and I don't need any of my model-fitting tricks. More engineering than science but nevertheless useful!</p><p style="text-align: justify;">To do the model fitting, I did a bunch of flying laps of the volcano circuit at constant power, with different physical parameters and varying power level each time. This route is fairly flat but not perfectly so, which means the average speed here will be a little bit lower than that achieved on truly flat ground, but probably typical of many flattish routes on Zwift such as Watopia's Waistband or Greater London Flat. I estimate the elevation/disequilibrium effect here to be around 0.5kph, so speeds achieved on Tempus Fugit may be about that much quicker than indicated here (or conversely, you'll hit a target pace with a bit less power than this formula suggests). Some of the riders in my data set are real, others imaginary. I've focussed mostly on women, first because I've been DS for my wife's team for a while, and also because through being a large reasonably fit man I can generate their racing power fairly comfortably for long enough to get a fix on their speeds. (Yes, I know there are software approaches to simulating the power. But it's something else to set up, and I don't really want to get into the world of power bots, you never know where it might lead...) Calculating the power needed for a large rider at high speed requires a bit of an extrapolation and may get less reliable. Bike is the Tron, I started out testing different bikes (to check on what zwiftinsider says) but the differences were too trivial to pursue. Specifically, the Canyon Aeroad 2021 with Zipp 808 wheels which I used to use a lot was just one second slower than the Tron. That's 0.1kph, equivalent to less than 2W.</p><p style="text-align: justify;">The black lines in the plot below are the model predictions for each rider, with the crosses marking the data points that I used to fit the model. Each line has 3 data points except for the top one which is my own physics. If someone wants to do a flying lap of the volcano at 450W (using my physical parameters) I'd love to know the result :-) The rest are mostly based around a women's team with jules being the bottom line. Few cyclists of either gender lie outside the range of our parameters! The model-data residuals are about 1.5W on average (RMS error) which is basically the magnitude of measurement error on the speed which is only precise to 0.1kph. This level of precision is plenty good enough for practical use, it's difficult to hit a power target more closely than about 5W anyway.</p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEio_quNLMpNmOpS91x62v3tUyWTmxMzMU5q9nn_HRwOxCISQi_jZqs45hRA0nnGRjxp0Ekys4BxylyBwUGIU3UUih-c-RKC_PVFIL_2vmS4ViKnxt9yScp6R5eXtwwc613SR7s/s1214/zwift_power.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="750" data-original-width="1214" height="396" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEio_quNLMpNmOpS91x62v3tUyWTmxMzMU5q9nn_HRwOxCISQi_jZqs45hRA0nnGRjxp0Ekys4BxylyBwUGIU3UUih-c-RKC_PVFIL_2vmS4ViKnxt9yScp6R5eXtwwc613SR7s/w640-h396/zwift_power.png" width="640" /></a></div><div class="separator" style="clear: both; text-align: justify;"><br /></div><p style="text-align: justify;">A conclusion that may be drawn is that for a medium-sized cyclist riding around 42kph, an extra 1kg of weight requires 2.5W more power to maintain the same speed (or alternatively, 1kg less saves 2.5W of power). For an additional 1cm of height, it's around 1W. These numbers aren't far from what I'd estimated through experience, it's nice to have them confirmed in a more careful calculation.</p>James Annanhttp://www.blogger.com/profile/04318741813895533700noreply@blogger.com9tag:blogger.com,1999:blog-9959776.post-34199983873604305572021-03-23T10:24:00.001+00:002021-03-23T11:00:11.414+00:00History in the (re)making?<p style="text-align: justify;">One year on and there's been a slew of articles revisiting the events of the past year. I was going to ask what has prompted this little flurry, but it's obviously the anniversary thing. With increasing pressure for a public inquiry, it seems that some of the key players have been trying to position themselves favourably, so let's have a look at what's been written, versus what the contemporaneous documentation actually says. SAGE minutes can be found <a href="https://www.gov.uk/government/collections/scientific-evidence-supporting-the-government-response-to-coronavirus-covid-19">here</a>, I think (I downloaded the relevant docs a while back).</p><p style="text-align: justify;">The first article I noticed was Laura Kuenssberg's “<a href="https://www.bbc.co.uk/news/uk-politics-56361599">Inside Story</a>”. She “<a href="https://twitter.com/bbclaurak/status/1371583263370842113">talked to more than 20 of the people who made the life and death decisions on Covid</a>”. The relevant passage that I am interested in concerns the decision making around mid-March:</p><p></p><blockquote><p style="text-align: justify;">“13 March, the government's Scientific Advisory Group for Emergencies (Sage) committee concluded the virus was spreading faster than thought.</p><p style="text-align: justify;">But it was Downing Street "modellers in the building", according to one current official, who pored again over the numbers, and realised the timetable that had only just been announced was likely to result in disaster.</p><p style="text-align: justify;">The next morning, a small group of key staff got together. Simple graphs were drawn on a whiteboard and the prime minister was confronted with the stark prediction that the plan he had just announced would result in the NHS collapsing under the sheer number of cases.</p><p style="text-align: justify;">Several of those present tell me that was the moment Mr Johnson realised the urgency - that the official assumptions about the speed of the spread of this new disease had been wrong.</p><p style="text-align: justify;">[...]</p><p style="text-align: justify;">On 16 March, the public were told to stop all unnecessary social contact and to work at home if possible.</p><p style="text-align: justify;">[...]</p><p style="text-align: justify;">For many inside government, the pace of change that week was staggering - but others remain frustrated the government machine, in their view, had failed to move quickly enough.”</p></blockquote><p></p><p style="text-align: justify;">The narrative being presented here of ponderous government is significantly misleading.</p><p style="text-align: justify;">The govt claimed at the time to be paying close attention to the scientific advice from SAGE, and the specific change to SAGE's assessment on the 13th March was not that the disease was spreading any more rapidly, but merely that the number of infections was higher than previously thought (due to greater importation from abroad). This is a key distinction that anyone numerate should be able to grasp readily. To quote from <a href="https://assets.publishing.service.gov.uk/government/uploads/system/uploads/attachment_data/file/888783/S0383_Fifteenth_SAGE_meeting_on_Wuhan_Coronavirus__Covid-19__.pdf">SAGE minutes on the 13th</a>:</p><p></p><blockquote style="text-align: justify;">“Owing to a 5-7 day lag in data provision for modelling, SAGE now believes there are more cases in the UK than SAGE previously expected at this point, and we may therefore be further ahead on the epidemic curve, but the UK remains on broadly the same epidemic trajectory and time to peak.<span style="text-align: left;"> </span></blockquote><blockquote style="text-align: justify;">[...]</blockquote><blockquote style="text-align: justify;">SAGE was unanimous that measures seeking to completely suppress spread of Covid- 19 will cause a second peak.”</blockquote><div style="text-align: justify;">Changing the estimate of the number of cases just brings the peak forward by a few days. Even a factor of 2 is only a single doubling time which they thought to be about 5-7 days at that time. Changing the estimate of the <i>growth rate</i> could (and in fact did) change the timetable and urgency much more significantly, but this didn't happen for another week and a half.</div><p style="text-align: justify;">It is not clear who “the modellers in the building” refers to in Kuenssberg's piece, but they are clearly not SAGE. Maybe Cummings had run a few numbers on a spreadsheet but since SAGE was supposed to be an assembly of world-leading experts, it would hardly be appropriate to discard their analyses in favour of his. For that matter, I had also blogged that the mitigation plan was likely to overwhelm the NHS (a conclusion that <a href="https://bskiesresearch.wordpress.com/2020/03/09/coronavirus/">I reached around the 9th March</a> based on some very simple calculations) but I wouldn't expect Johnson to listen to me either. SAGE minutes are very clear that they still believed the doubling rate to be 5-7 days right up to the 18th March and had described any overload on the NHS as being some way off (albeit a looming problem that would need addressing at some time in the future). They were unanimously (see above) opposed to suppression at this point.</p><p style="text-align: justify;">On the <a href="https://assets.publishing.service.gov.uk/government/uploads/system/uploads/attachment_data/file/888784/S0384_Sixteenth_SAGE_meeting_on_Wuhan_Coronavirus__Covid-19__.pdf">16th, the SAGE meeting</a> changed its advice somewhat and suggested that some social distancing measures (but not school closures) should be implemented promptly:</p><p></p><blockquote style="text-align: justify;">“SAGE advises that there is clear evidence to support additional social distancing measures be introduced as soon as possible.</blockquote><blockquote style="text-align: justify;">[...]</blockquote><p></p><div><div></div></div><blockquote><div><div style="text-align: justify;">SAGE will further review at its next meeting whether, in the light of new data, school closures may also be required to prevent NHS capacity being exceeded.”</div></div><div></div></blockquote><div style="text-align: justify;">Clearly there was some increased urgency here but NOT any indication that the NHS was under immediate threat, in direct contradiction to Kuenssberg's unattributed claim above that “the prime minister was confronted with the stark prediction that the plan he had just announced would result in the NHS collapsing under the sheer number of cases.” I'm not saying it is impossible that anyone said such a thing, but if they did, they were an isolated voice and certainly not representative of SAGE as a whole.</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">Immediately following the SAGE meeting on the 16th, the Govt did of course request that people avoid all unnecessary social contact. Admittedly, this instruction had neither legal force nor economic support at that point but SAGE was obviously reasonably satisfied with the adequacy of this plan as can be seen from their <a href="https://assets.publishing.service.gov.uk/government/uploads/system/uploads/attachment_data/file/888785/S0385_Seventeenth_SAGE_meeting_on_Covid-19_.pdf">minutes of the 18th</a> (at which time they also recommended school closures):</div><div><div><blockquote style="text-align: justify;">“SAGE advises that the measures already announced should have a significant effect, provided compliance rates are good and in line with the assumptions. Additional measures will be needed if compliance rates are low.”</blockquote></div></div><div style="text-align: justify;">So it was only in the case of poor compliance that additional measures would be required.</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">There was no SAGE meeting between 18th and 23rd, which was unfortunate in the circumstances (21-22 being a weekend). On the 23rd, SAGE finally realised that they had got the R number wrong and that as a result the doubling time was much shorter than had been previously believed, making the situation quite desperate. Specifically, the <a href="https://assets.publishing.service.gov.uk/government/uploads/system/uploads/attachment_data/file/888787/S0386_Eighteenth_SAGE_meeting_on_Covid-19_.pdf">SAGE meeting of the 23rd</a> concluded: “Case numbers could exceed NHS capacity within the next 10 days on the current trajectory” and this statement must be understood in the context of the immediately preceding <a href="https://assets.publishing.service.gov.uk/government/uploads/system/uploads/attachment_data/file/887463/24-spi-m-o-consensus-view-20032020.pdf">20th March SPI-M meeting</a> which noted both: “Any measures enacted would take 2-3 weeks to have an impact on ICU admissions” and also: “If the higher reproduction number is representative of the longer term, then it is likely that additional measures will be required to bring it below one”.</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">Thus SAGE's underestimate of the R number didn't just mean that the epidemic was coming faster and harder than previously thought: another consequence is that actions that would have been adequate for R=2.4, might not be adequate for R=3. It is quite understandable that this caused alarm within SAGE, but it only happened on the 23rd.</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">The Govt imposed a legally-enforceable lockdown with much more far-reaching restrictions immediately that evening (23rd March).</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">Moving on to the next article, in <a href="https://www.theguardian.com/uk-news/2021/mar/19/patrick-vallance-adviser-scientific-truth-to-power">the Guardian</a>, a hagiography of Patrick Vallance:</div><p></p><blockquote><p style="text-align: justify;">“But it now seems clear that Boris Johnson, and his advisers, were slow to heed Vallance’s early advice.</p><p style="text-align: justify;">Before the 16 March press conference, Vallance chaired a meeting of the Scientific Advisory Group for Emergencies (Sage) in which a collection of experts had advised that the first lockdown should begin immediately.</p><p style="text-align: justify;">Johnson did not announce the unprecedented national lockdown until a week later on 23 March in a primetime TV address to the nation.”</p></blockquote><p style="text-align: justify;">This is simply not true as documented above. SAGE asked for relatively modest action around the 16-18th, and the Govt responded promptly. SAGE explicitly assessed on the 18th that the actions were probably adequate and it was only on the 23rd when they realised that they had got the doubling time wrong, that they suddenly realised they had a much larger and more urgent problem on their hands. Vallance also got this wrong in <a href="https://julesandjames.blogspot.com/2020/07/patrick-vallances-faulty-memory.html">his appearance before the House of Commons Select Committee on Science and Technology</a>. </p><p style="text-align: justify;">Most recently, a <a href="https://www.theguardian.com/news/audio/2021/mar/22/neil-ferguson-covid-year-shattered-way-of-life-podcast">podcast on the Guardian</a> consisting of an interview of Neil Ferguson. He points very firmly to the data about higher case numbers due to greater importation being what drove the accelerated decision making in mid-March (NB this view is very different from Vallance who very emphatically linked the change in policy advice to the revision of the estimated doubling time - it is simply not possible for both Ferguson and Vallance to both be correct about this). Ferguson mentions this being discussed in the “first weekend in March” which I'm sure must be a simple slip as this would be 7-8th March whereas on the 10th and even 13th SAGE seems pretty sanguine about the situation and does not suggest any need to take immediate action. Assuming he meant the 14-15th March instead, this is far more consistent with SAGE as the minutes of the 16th do certainly suggest some some action should be taken in the light of the new data:</p><p></p><blockquote style="text-align: justify;">“The science suggests additional social distancing measures should be introduced as soon as possible.”</blockquote><p></p><p style="text-align: justify;">When asked specifically (at 11m20 in the podcast) “were scientists telling ministers to go earlier?” Ferguson firstly points again to the surveillance data as escalating the decision making process, and then coyly says it was entirely in the Govt's hands as to what actions they took. He could have said, but chose not to, that the Govt followed SAGE's advice promptly and to the letter. And the interviewer didn't pursue the point. While the improved surveillance data undoubtedly played a role in the process, the urgent advice for the most stringent controls only came on the 23rd as a result of the revised estimate of doubling time. You only have to glance at the SAGE minutes to see that they were not shy about offering policy advice throughout the outbreak.</p><p style="text-align: justify;">At 16m40 onwards the interviewer says, with reference to the situation in September after schools reopened: </p><p></p><blockquote style="text-align: justify;">“...once again the advice from scientists was to lock down. But that advice was not heeded. Did that delay once again lead to a higher death rate than we might have seen?”</blockquote><p style="text-align: justify;">Without getting into the September story here, any delayed response from the Govt (which I don't dispute was evident in the autumn) could only “once again” have resulted in a higher death rate if there had <i>also</i> been a delayed response to advice to lock down in March. Which there was not, according to the evidence I have outlined.</p><span><a name='more'></a></span><p style="text-align: justify;">On reading the minutes again (and again and again), I can see how some of the protagonists might have managed to confabulate a story in which they were pressing for action in mid-March and the govt was slow to respond. From the 13th onwards, there is some recognition by SAGE that the epidemic is a bit more advanced than they had thought (but not at that time any acknowledgement that the doubling time was much shorter than they had estimated). There is mention of increased (but not imminent) threat to the NHS and a clear, albeit measured, ramping up of urgency through the minutes of the 16th and 18th. However the measures called for were limited and the govt responded promptly, with SAGE on the 18th only saying that further action would be needed “if compliance rates are low” (which they were not). It may well have been the case that individuals within the room were calling for stronger action, but if so, SAGE did not support this. It probably only requires a relatively small leap of imagination to create a false memory in which the advanced status of the outbreak by the 13th or 16th alarmed SAGE sufficiently to ask for a lockdown. However this doesn't make it true and the minutes tell the story very clearly. It is only on the <a href="https://assets.publishing.service.gov.uk/government/uploads/system/uploads/attachment_data/file/887463/24-spi-m-o-consensus-view-20032020.pdf">20th March that SPI-M-O finally realised</a> that the R number was significantly higher than they had previously said, meaning that (i) the doubling time of the outbreak was considerably shorter, (ii) current measures were likely inadequate and (iii) the NHS was about to be overwhelmed. This information only reached SAGE on the <a href="https://assets.publishing.service.gov.uk/government/uploads/system/uploads/attachment_data/file/888787/S0386_Eighteenth_SAGE_meeting_on_Covid-19_.pdf">23rd March</a>.</p><p style="text-align: justify;">The reluctance of journalists to tell this story accurately is....curious.</p><p></p><p></p>James Annanhttp://www.blogger.com/profile/04318741813895533700noreply@blogger.com2tag:blogger.com,1999:blog-9959776.post-35670184803769900852021-03-01T09:00:00.001+00:002021-03-01T09:00:00.920+00:00BlueSkiesResearch.org.uk: Escape velocity <p class="has-text-align-justify">There is currently lot of debate on how and when we lift restrictions, and the risks of this. There are several unknowns that may affect the outcome. I have extended the model in a couple of simple ways, firstly by including a vaccination effect which both immunises people, and substantially reduces the fatality rate of those who do get ill, and also by including a loss of immunity over time which is potentially important for longer simulations. The magnitudes of these effects seem highly uncertain, I’ve just made what seems like plausible guesstimates. I use a vaccination rate of 0.5% per day which is probably in the right ballpark though my implementation is extremely simplistic (NB this is the rate at which people move from the vulnerable to the immune category, so it directly accounts for the imperfect performance of the vaccine itself). As well as this, I’m assuming the fatality rate for those infected drops down to 0.3% as vaccination progresses through the most vulnerable groups, since we’ve heard so many good things about vaccination preventing serious illness even in those who do get ill. This value must also account for the proportion of victims that have not been vaccinated at all, so it’s really a bit of a guess but the right answer has to be significantly lower than the original fatality rate. The loss of immunity in this model occurs on a 1 year time scale, which in practice due to model structure means 1/365 = 0.27% of the immune population return to the vulnerable state each day. I don’t claim these numbers are correct, I merely hope that they are not wrong by a factor of more than about 2. In the long term in the absence of illness, the balance between vaccination and loss of immunity loss would lead to about 1/3rd of the population being vulnerable and 2/3rds being immune at any given time. This is just about enough to permanently suppress the disease (assuming R0=3), or at least keep it at a very low level.</p> <p class="has-text-align-justify">The model simulates the historical trajectory rather well and also matches the ONS and REACT data sets, as I’ve shown previously, so I think it’s broadly reasonable. The recent announcements amount to an opening of schools on the 8th March, and then a subsequent reopening of wider society over the following weeks and months. In the simulations I’m about to present, I’m testing the proposition that we can open up society back to a near-normal situation more quickly. So after bumping the R number up on the 8th March I then increase it again more substantially, putting the underlying R0 number up to 2.5 in the ensemble mean, close to (but still lower than) the value it took at the start of last year, with the intention being to simulate a return to near-normal conditions but with the assumption that some people will still tend to be a bit on the cautious side. So this is a much more ambitious plan than the Govt is aiming for. I’m really just having a look to see what the model does under this fairly severe test. Here is the graph of case numbers when I bump the R number up at the end of April:</p> <figure class="wp-block-image size-large"><a href="https://bskiesresearch.files.wordpress.com/2021/02/uk_24_feb_2021_extension_moredeath_later_c.png"><img alt="" class="wp-image-1837" data-attachment-id="1837" data-comments-opened="1" data-image-description="" data-image-meta="{"aperture":"0","credit":"","camera":"","caption":"","created_timestamp":"0","copyright":"","focal_length":"0","iso":"0","shutter_speed":"0","title":"","orientation":"0"}" data-image-title="uk_24_feb_2021_extension_moredeath_later_c" data-large-file="https://bskiesresearch.files.wordpress.com/2021/02/uk_24_feb_2021_extension_moredeath_later_c.png?w=700" data-medium-file="https://bskiesresearch.files.wordpress.com/2021/02/uk_24_feb_2021_extension_moredeath_later_c.png?w=300" data-orig-file="https://bskiesresearch.files.wordpress.com/2021/02/uk_24_feb_2021_extension_moredeath_later_c.png" data-orig-size="1102,681" data-permalink="https://bskiesresearch.wordpress.com/uk_24_feb_2021_extension_moredeath_later_c/" height="395" sizes="(max-width: 1024px) 100vw, 1024px" src="https://bskiesresearch.files.wordpress.com/2021/02/uk_24_feb_2021_extension_moredeath_later_c.png?w=1024" srcset="https://bskiesresearch.files.wordpress.com/2021/02/uk_24_feb_2021_extension_moredeath_later_c.png?w=1024 1024w, https://bskiesresearch.files.wordpress.com/2021/02/uk_24_feb_2021_extension_moredeath_later_c.png?w=150 150w, https://bskiesresearch.files.wordpress.com/2021/02/uk_24_feb_2021_extension_moredeath_later_c.png?w=300 300w, https://bskiesresearch.files.wordpress.com/2021/02/uk_24_feb_2021_extension_moredeath_later_c.png?w=768 768w, https://bskiesresearch.files.wordpress.com/2021/02/uk_24_feb_2021_extension_moredeath_later_c.png 1102w" width="640" /></a></figure> <p>And here is the equivalent for deaths, which also shows how the R number rises:</p> <figure class="wp-block-image size-large"><a href="https://bskiesresearch.files.wordpress.com/2021/02/uk_24_feb_2021_extension_moredeath_later_d.png"><img alt="" class="wp-image-1838" data-attachment-id="1838" data-comments-opened="1" data-image-description="" data-image-meta="{"aperture":"0","credit":"","camera":"","caption":"","created_timestamp":"0","copyright":"","focal_length":"0","iso":"0","shutter_speed":"0","title":"","orientation":"0"}" data-image-title="uk_24_feb_2021_extension_moredeath_later_d" data-large-file="https://bskiesresearch.files.wordpress.com/2021/02/uk_24_feb_2021_extension_moredeath_later_d.png?w=700" data-medium-file="https://bskiesresearch.files.wordpress.com/2021/02/uk_24_feb_2021_extension_moredeath_later_d.png?w=300" data-orig-file="https://bskiesresearch.files.wordpress.com/2021/02/uk_24_feb_2021_extension_moredeath_later_d.png" data-orig-size="1102,681" data-permalink="https://bskiesresearch.wordpress.com/uk_24_feb_2021_extension_moredeath_later_d/" height="395" sizes="(max-width: 1024px) 100vw, 1024px" src="https://bskiesresearch.files.wordpress.com/2021/02/uk_24_feb_2021_extension_moredeath_later_d.png?w=1024" srcset="https://bskiesresearch.files.wordpress.com/2021/02/uk_24_feb_2021_extension_moredeath_later_d.png?w=1024 1024w, https://bskiesresearch.files.wordpress.com/2021/02/uk_24_feb_2021_extension_moredeath_later_d.png?w=150 150w, https://bskiesresearch.files.wordpress.com/2021/02/uk_24_feb_2021_extension_moredeath_later_d.png?w=300 300w, https://bskiesresearch.files.wordpress.com/2021/02/uk_24_feb_2021_extension_moredeath_later_d.png?w=768 768w, https://bskiesresearch.files.wordpress.com/2021/02/uk_24_feb_2021_extension_moredeath_later_d.png 1102w" width="640" /></a></figure> <p>So there is another wave of sorts, but not a terrible one compared to what we’ve seen. In many simulations the death toll does not go over 100 per day though it does go on a long time. Sorry for the messy annotations on the plots, I can’t be bothered adjusting the text position as the run length changes.</p> <p>If we bring the opening forward to the end of March, it’s significantly worse, due to lower vaccination coverage at that point:</p> <figure class="wp-block-image size-large"><a href="https://bskiesresearch.files.wordpress.com/2021/02/uk_24_feb_2021_extension_moredeath_d.png"><img alt="" class="wp-image-1840" data-attachment-id="1840" data-comments-opened="1" data-image-description="" data-image-meta="{"aperture":"0","credit":"","camera":"","caption":"","created_timestamp":"0","copyright":"","focal_length":"0","iso":"0","shutter_speed":"0","title":"","orientation":"0"}" data-image-title="uk_24_feb_2021_extension_moredeath_d" data-large-file="https://bskiesresearch.files.wordpress.com/2021/02/uk_24_feb_2021_extension_moredeath_d.png?w=700" data-medium-file="https://bskiesresearch.files.wordpress.com/2021/02/uk_24_feb_2021_extension_moredeath_d.png?w=300" data-orig-file="https://bskiesresearch.files.wordpress.com/2021/02/uk_24_feb_2021_extension_moredeath_d.png" data-orig-size="1102,681" data-permalink="https://bskiesresearch.wordpress.com/uk_24_feb_2021_extension_moredeath_d/" height="395" sizes="(max-width: 1024px) 100vw, 1024px" src="https://bskiesresearch.files.wordpress.com/2021/02/uk_24_feb_2021_extension_moredeath_d.png?w=1024" srcset="https://bskiesresearch.files.wordpress.com/2021/02/uk_24_feb_2021_extension_moredeath_d.png?w=1024 1024w, https://bskiesresearch.files.wordpress.com/2021/02/uk_24_feb_2021_extension_moredeath_d.png?w=150 150w, https://bskiesresearch.files.wordpress.com/2021/02/uk_24_feb_2021_extension_moredeath_d.png?w=300 300w, https://bskiesresearch.files.wordpress.com/2021/02/uk_24_feb_2021_extension_moredeath_d.png?w=768 768w, https://bskiesresearch.files.wordpress.com/2021/02/uk_24_feb_2021_extension_moredeath_d.png 1102w" width="640" /></a></figure> <p>Here the daily deaths goes well over 100 for most simulations and can reach 1000 in the worse cases. On the other hand, if we put off the opening up for another couple of months to the end of July, the picture is very much better, both for cases:</p> <figure class="wp-block-image size-large"><a href="https://bskiesresearch.files.wordpress.com/2021/02/uk_24_feb_2021_extension_moredeath_muchlater_c.png"><img alt="" class="wp-image-1848" data-attachment-id="1848" data-comments-opened="1" data-image-description="" data-image-meta="{"aperture":"0","credit":"","camera":"","caption":"","created_timestamp":"0","copyright":"","focal_length":"0","iso":"0","shutter_speed":"0","title":"","orientation":"0"}" data-image-title="uk_24_feb_2021_extension_moredeath_muchlater_c" data-large-file="https://bskiesresearch.files.wordpress.com/2021/02/uk_24_feb_2021_extension_moredeath_muchlater_c.png?w=700" data-medium-file="https://bskiesresearch.files.wordpress.com/2021/02/uk_24_feb_2021_extension_moredeath_muchlater_c.png?w=300" data-orig-file="https://bskiesresearch.files.wordpress.com/2021/02/uk_24_feb_2021_extension_moredeath_muchlater_c.png" data-orig-size="1102,681" data-permalink="https://bskiesresearch.wordpress.com/uk_24_feb_2021_extension_moredeath_muchlater_c/" height="395" sizes="(max-width: 1024px) 100vw, 1024px" src="https://bskiesresearch.files.wordpress.com/2021/02/uk_24_feb_2021_extension_moredeath_muchlater_c.png?w=1024" srcset="https://bskiesresearch.files.wordpress.com/2021/02/uk_24_feb_2021_extension_moredeath_muchlater_c.png?w=1024 1024w, https://bskiesresearch.files.wordpress.com/2021/02/uk_24_feb_2021_extension_moredeath_muchlater_c.png?w=150 150w, https://bskiesresearch.files.wordpress.com/2021/02/uk_24_feb_2021_extension_moredeath_muchlater_c.png?w=300 300w, https://bskiesresearch.files.wordpress.com/2021/02/uk_24_feb_2021_extension_moredeath_muchlater_c.png?w=768 768w, https://bskiesresearch.files.wordpress.com/2021/02/uk_24_feb_2021_extension_moredeath_muchlater_c.png 1102w" width="640" /></a></figure> <p>and deaths:</p> <figure class="wp-block-image size-large"><a href="https://bskiesresearch.files.wordpress.com/2021/02/uk_24_feb_2021_extension_moredeath_muchlater_d.png"><img alt="" class="wp-image-1849" data-attachment-id="1849" data-comments-opened="1" data-image-description="" data-image-meta="{"aperture":"0","credit":"","camera":"","caption":"","created_timestamp":"0","copyright":"","focal_length":"0","iso":"0","shutter_speed":"0","title":"","orientation":"0"}" data-image-title="uk_24_feb_2021_extension_moredeath_muchlater_d" data-large-file="https://bskiesresearch.files.wordpress.com/2021/02/uk_24_feb_2021_extension_moredeath_muchlater_d.png?w=700" data-medium-file="https://bskiesresearch.files.wordpress.com/2021/02/uk_24_feb_2021_extension_moredeath_muchlater_d.png?w=300" data-orig-file="https://bskiesresearch.files.wordpress.com/2021/02/uk_24_feb_2021_extension_moredeath_muchlater_d.png" data-orig-size="1102,681" data-permalink="https://bskiesresearch.wordpress.com/uk_24_feb_2021_extension_moredeath_muchlater_d/" height="395" sizes="(max-width: 1024px) 100vw, 1024px" src="https://bskiesresearch.files.wordpress.com/2021/02/uk_24_feb_2021_extension_moredeath_muchlater_d.png?w=1024" srcset="https://bskiesresearch.files.wordpress.com/2021/02/uk_24_feb_2021_extension_moredeath_muchlater_d.png?w=1024 1024w, https://bskiesresearch.files.wordpress.com/2021/02/uk_24_feb_2021_extension_moredeath_muchlater_d.png?w=150 150w, https://bskiesresearch.files.wordpress.com/2021/02/uk_24_feb_2021_extension_moredeath_muchlater_d.png?w=300 300w, https://bskiesresearch.files.wordpress.com/2021/02/uk_24_feb_2021_extension_moredeath_muchlater_d.png?w=768 768w, https://bskiesresearch.files.wordpress.com/2021/02/uk_24_feb_2021_extension_moredeath_muchlater_d.png 1102w" width="640" /></a></figure> <p class="has-text-align-justify">While there are still a few ensemble members generating 100 deaths per day, the median is down at 1, implying a substantial probability that the disease is basically suppressed at that point.</p> <p class="has-text-align-justify">I have to emphasise the large number of simplifications and guesstimates in this modelling. It does however suggest that an over-rapid opening is a significant risk and there are likely benefits to hanging on a bit longer than some might like in order that more people can be vaccinated. My results seems broadly in line with the more sophisticated modelling that was <a href="https://www.theguardian.com/world/2021/feb/22/relaxing-covid-rules-too-early-likely-to-bring-huge-death-toll-scientists-say">in the media a few days ago</a>. To be honest it’s not far from what you would get out of a back-of-the-envelope calculation based on numbers that are thought to be immune vs vulnerable and the R0 number you expect to arise from social mixing, but for better or worse a full model calculation is probably a bit more convincing. </p> <p class="has-text-align-justify">While the Govt plan seems broadly reasonable to me, there are still substantial uncertainties in how things will play out and it is vitally important that the govt should pay attention to the data and be prepared to shift the proposed dates in the light of evidence that accrues over the coming weeks. Unfortunately history suggests this behaviour is unlikely to occur, but we can live in hope.</p> James Annanhttp://www.blogger.com/profile/04318741813895533700noreply@blogger.com0tag:blogger.com,1999:blog-9959776.post-60436909977984958602021-01-19T07:44:00.000+00:002021-01-19T07:44:00.066+00:00BlueSkiesResearch.org.uk: So near and yet not quite…<p class="has-text-align-justify">There’s been quite an amazing turnaround since <a href="https://bskiesresearch.wordpress.com/2021/01/04/not-even-half-way-there/">my last blog post</a>. At the time I wrote that, the Govt was insisting that schools would open as planned (indeed they did open the very next day), and that another lockdown was unthinkable. So my grim simulations were performed on that basis.</p> <p class="has-text-align-justify">Of course, the next evening, we had another u-turn… schools shut immediately and many other restrictions were introduced on social mixing. Even so, most of the experts thought we would be in for a rough time, and I didn’t see any reason to disagree with them. The new variant had been spreading fast and no-one was confident that the restrictions would be enough to suppress it. Vaccination was well behind schedule (who remembers <a href="https://www.politicshome.com/news/article/boris-johnson-covid-19-pfizer-trial">10 million doses by the end of the year?</a>) and could not catch up exponential growth of the virus.</p> <p class="has-text-align-justify">Just after I posted that blog, someone pointed me to <a href="https://cmmid.github.io/topics/covid19/uk-novel-variant.html">this paper from LSHTM</a> which generated broadly similar results with much more detailed modelling. Their scenarios all predicted about 100k additional deaths in the spring, with the exception of one optimistic case where stiff restrictions starting in mid-December, coupled to very rapid vaccination, could cut this number to 30-40k. Given that we were already in Jan with no lockdown and little vaccination in sight, this seemed out of reach. Here is the table that summarises their projections. Note that their “total deaths” is the total within this time frame, not total for the epidemic.</p> <figure class="wp-block-image size-large"><a href="https://bskiesresearch.files.wordpress.com/2021/01/screen-shot-2021-01-18-at-11.54.41.png"><img alt="" class="wp-image-1818" data-attachment-id="1818" data-comments-opened="1" data-image-description="" data-image-meta="{"aperture":"0","credit":"","camera":"","caption":"","created_timestamp":"0","copyright":"","focal_length":"0","iso":"0","shutter_speed":"0","title":"","orientation":"0"}" data-image-title="screen-shot-2021-01-18-at-11.54.41" data-large-file="https://bskiesresearch.files.wordpress.com/2021/01/screen-shot-2021-01-18-at-11.54.41.png?w=700" data-medium-file="https://bskiesresearch.files.wordpress.com/2021/01/screen-shot-2021-01-18-at-11.54.41.png?w=300" data-orig-file="https://bskiesresearch.files.wordpress.com/2021/01/screen-shot-2021-01-18-at-11.54.41.png" data-orig-size="1906,1016" data-permalink="https://bskiesresearch.wordpress.com/screen-shot-2021-01-18-at-11-54-41/" height="341" sizes="(max-width: 1024px) 100vw, 1024px" src="https://bskiesresearch.files.wordpress.com/2021/01/screen-shot-2021-01-18-at-11.54.41.png?w=1024" srcset="https://bskiesresearch.files.wordpress.com/2021/01/screen-shot-2021-01-18-at-11.54.41.png?w=1024 1024w, https://bskiesresearch.files.wordpress.com/2021/01/screen-shot-2021-01-18-at-11.54.41.png?w=150 150w, https://bskiesresearch.files.wordpress.com/2021/01/screen-shot-2021-01-18-at-11.54.41.png?w=300 300w, https://bskiesresearch.files.wordpress.com/2021/01/screen-shot-2021-01-18-at-11.54.41.png?w=768 768w, https://bskiesresearch.files.wordpress.com/2021/01/screen-shot-2021-01-18-at-11.54.41.png 1906w" width="640" /></a></figure> <p class="has-text-align-justify">However, since that point, cases have dropped very sharply indeed. Better than in the most optimistic scenario of LSHTM who anticipated R dropping to a little below 1. Deaths have not peaked quite yet but my modelling predicts this should happen quite soon and then we may see them fall quite rapidly. The future under suppression looks very different to what it did a couple of weeks ago.</p> <p class="has-text-align-justify">So this was the model fit I did back on 3rd Jan, which assumes no lockdown. Left is cases, right is deaths which rises to well over 1k per day for a large part of early 2021.</p> <div class="wp-block-jetpack-tiled-gallery aligncenter is-style-rectangular" data-carousel-extra="{"blog_id":60752427,"permalink":"https:\/\/bskiesresearch.wordpress.com\/2021\/01\/18\/so-near-and-yet-not-quite\/"}"><div class="tiled-gallery__gallery" data-carousel-extra="{"blog_id":60752427,"permalink":"https:\/\/bskiesresearch.wordpress.com\/2021\/01\/18\/so-near-and-yet-not-quite\/"}"><div class="tiled-gallery__row" data-carousel-extra="{"blog_id":60752427,"permalink":"https:\/\/bskiesresearch.wordpress.com\/2021\/01\/18\/so-near-and-yet-not-quite\/"}"><div class="tiled-gallery__col" data-carousel-extra="{"blog_id":60752427,"permalink":"https:\/\/bskiesresearch.wordpress.com\/2021\/01\/18\/so-near-and-yet-not-quite\/"}" style="flex-basis: 50%;"><figure class="tiled-gallery__item"><img alt="" data-attachment-id="1805" data-comments-opened="1" data-height="761" data-id="1805" data-image-description="" data-image-meta="{"aperture":"0","credit":"","camera":"","caption":"","created_timestamp":"0","copyright":"","focal_length":"0","iso":"0","shutter_speed":"0","title":"","orientation":"0"}" data-image-title="uk_03_jan_2021_c" data-large-file="https://bskiesresearch.files.wordpress.com/2021/01/uk_03_jan_2021_c.png?w=700" data-link="https://bskiesresearch.wordpress.com/uk_03_jan_2021_c/" data-medium-file="https://bskiesresearch.files.wordpress.com/2021/01/uk_03_jan_2021_c.png?w=300" data-orig-file="https://bskiesresearch.files.wordpress.com/2021/01/uk_03_jan_2021_c.png" data-orig-size="1232,761" data-permalink="https://bskiesresearch.wordpress.com/uk_03_jan_2021_c/" data-url="https://bskiesresearch.files.wordpress.com/2021/01/uk_03_jan_2021_c.png" data-width="1232" height="247" src="https://bskiesresearch.files.wordpress.com/2021/01/uk_03_jan_2021_c.png" srcset="https://bskiesresearch.files.wordpress.com/2021/01/uk_03_jan_2021_c.png?strip=info&w=600 600w,https://bskiesresearch.files.wordpress.com/2021/01/uk_03_jan_2021_c.png?strip=info&w=761 761w" width="400" /></figure></div><div class="tiled-gallery__col" data-carousel-extra="{"blog_id":60752427,"permalink":"https:\/\/bskiesresearch.wordpress.com\/2021\/01\/18\/so-near-and-yet-not-quite\/"}" style="flex-basis: 50%;"><figure class="tiled-gallery__item"><img alt="" data-attachment-id="1806" data-comments-opened="1" data-height="761" data-id="1806" data-image-description="" data-image-meta="{"aperture":"0","credit":"","camera":"","caption":"","created_timestamp":"0","copyright":"","focal_length":"0","iso":"0","shutter_speed":"0","title":"","orientation":"0"}" data-image-title="uk_03_jan_2021_d" data-large-file="https://bskiesresearch.files.wordpress.com/2021/01/uk_03_jan_2021_d.png?w=700" data-link="https://bskiesresearch.wordpress.com/uk_03_jan_2021_d/" data-medium-file="https://bskiesresearch.files.wordpress.com/2021/01/uk_03_jan_2021_d.png?w=300" data-orig-file="https://bskiesresearch.files.wordpress.com/2021/01/uk_03_jan_2021_d.png" data-orig-size="1232,761" data-permalink="https://bskiesresearch.wordpress.com/uk_03_jan_2021_d/" data-url="https://bskiesresearch.files.wordpress.com/2021/01/uk_03_jan_2021_d.png" data-width="1232" height="247" src="https://bskiesresearch.files.wordpress.com/2021/01/uk_03_jan_2021_d.png" srcset="https://bskiesresearch.files.wordpress.com/2021/01/uk_03_jan_2021_d.png?strip=info&w=600 600w,https://bskiesresearch.files.wordpress.com/2021/01/uk_03_jan_2021_d.png?strip=info&w=761 761w" width="400" /></figure></div></div></div></div> <p class="has-text-align-justify">And here are the cumulative median infections and deaths corresponding to the above, with some grid lines marked on to indicate what was in store up to the end of Feb (for infections) and end of March (for deaths). As you can see, about 100k of the latter in this time frame (ie 186-73 = 113k additional deaths).</p> <div class="wp-block-jetpack-tiled-gallery aligncenter is-style-rectangular" data-carousel-extra="{"blog_id":60752427,"permalink":"https:\/\/bskiesresearch.wordpress.com\/2021\/01\/18\/so-near-and-yet-not-quite\/"}"><div class="tiled-gallery__gallery" data-carousel-extra="{"blog_id":60752427,"permalink":"https:\/\/bskiesresearch.wordpress.com\/2021\/01\/18\/so-near-and-yet-not-quite\/"}"><div class="tiled-gallery__row" data-carousel-extra="{"blog_id":60752427,"permalink":"https:\/\/bskiesresearch.wordpress.com\/2021\/01\/18\/so-near-and-yet-not-quite\/"}"><div class="tiled-gallery__col" data-carousel-extra="{"blog_id":60752427,"permalink":"https:\/\/bskiesresearch.wordpress.com\/2021\/01\/18\/so-near-and-yet-not-quite\/"}" style="flex-basis: 50%;"><figure class="tiled-gallery__item"><img alt="" data-attachment-id="1812" data-comments-opened="1" data-height="775" data-id="1812" data-image-description="" data-image-meta="{"aperture":"0","credit":"","camera":"","caption":"","created_timestamp":"0","copyright":"","focal_length":"0","iso":"0","shutter_speed":"0","title":"","orientation":"0"}" data-image-title="total_inf_03_jan_2021-2" data-large-file="https://bskiesresearch.files.wordpress.com/2021/01/total_inf_03_jan_2021-2.png?w=700" data-link="https://bskiesresearch.wordpress.com/total_inf_03_jan_2021-2/" data-medium-file="https://bskiesresearch.files.wordpress.com/2021/01/total_inf_03_jan_2021-2.png?w=300" data-orig-file="https://bskiesresearch.files.wordpress.com/2021/01/total_inf_03_jan_2021-2.png" data-orig-size="1254,775" data-permalink="https://bskiesresearch.wordpress.com/total_inf_03_jan_2021-2/" data-url="https://bskiesresearch.files.wordpress.com/2021/01/total_inf_03_jan_2021-2.png" data-width="1254" height="247" src="https://bskiesresearch.files.wordpress.com/2021/01/total_inf_03_jan_2021-2.png" srcset="https://bskiesresearch.files.wordpress.com/2021/01/total_inf_03_jan_2021-2.png?strip=info&w=600 600w,https://bskiesresearch.files.wordpress.com/2021/01/total_inf_03_jan_2021-2.png?strip=info&w=775 775w" width="400" /></figure></div><div class="tiled-gallery__col" data-carousel-extra="{"blog_id":60752427,"permalink":"https:\/\/bskiesresearch.wordpress.com\/2021\/01\/18\/so-near-and-yet-not-quite\/"}" style="flex-basis: 50%;"><figure class="tiled-gallery__item"><img alt="" data-attachment-id="1813" data-comments-opened="1" data-height="775" data-id="1813" data-image-description="" data-image-meta="{"aperture":"0","credit":"","camera":"","caption":"","created_timestamp":"0","copyright":"","focal_length":"0","iso":"0","shutter_speed":"0","title":"","orientation":"0"}" data-image-title="total_death_03_jan_2021" data-large-file="https://bskiesresearch.files.wordpress.com/2021/01/total_death_03_jan_2021.png?w=700" data-link="https://bskiesresearch.wordpress.com/total_death_03_jan_2021/" data-medium-file="https://bskiesresearch.files.wordpress.com/2021/01/total_death_03_jan_2021.png?w=300" data-orig-file="https://bskiesresearch.files.wordpress.com/2021/01/total_death_03_jan_2021.png" data-orig-size="1254,775" data-permalink="https://bskiesresearch.wordpress.com/total_death_03_jan_2021/" data-url="https://bskiesresearch.files.wordpress.com/2021/01/total_death_03_jan_2021.png" data-width="1254" height="247" src="https://bskiesresearch.files.wordpress.com/2021/01/total_death_03_jan_2021.png" srcset="https://bskiesresearch.files.wordpress.com/2021/01/total_death_03_jan_2021.png?strip=info&w=600 600w,https://bskiesresearch.files.wordpress.com/2021/01/total_death_03_jan_2021.png?strip=info&w=775 775w" width="400" /></figure></div></div></div></div> <p class="has-text-align-justify">Here now are the graphs of the latest model fit showing the extremely rapid drop in cases and predicted drop in deaths assuming a 6 week lockdown:</p> <div class="wp-block-jetpack-tiled-gallery aligncenter is-style-rectangular" data-carousel-extra="{"blog_id":60752427,"permalink":"https:\/\/bskiesresearch.wordpress.com\/2021\/01\/18\/so-near-and-yet-not-quite\/"}"><div class="tiled-gallery__gallery" data-carousel-extra="{"blog_id":60752427,"permalink":"https:\/\/bskiesresearch.wordpress.com\/2021\/01\/18\/so-near-and-yet-not-quite\/"}"><div class="tiled-gallery__row" data-carousel-extra="{"blog_id":60752427,"permalink":"https:\/\/bskiesresearch.wordpress.com\/2021\/01\/18\/so-near-and-yet-not-quite\/"}"><div class="tiled-gallery__col" data-carousel-extra="{"blog_id":60752427,"permalink":"https:\/\/bskiesresearch.wordpress.com\/2021\/01\/18\/so-near-and-yet-not-quite\/"}" style="flex-basis: 50%;"><figure class="tiled-gallery__item"><img alt="" data-attachment-id="1810" data-comments-opened="1" data-height="681" data-id="1810" data-image-description="" data-image-meta="{"aperture":"0","credit":"","camera":"","caption":"","created_timestamp":"0","copyright":"","focal_length":"0","iso":"0","shutter_speed":"0","title":"","orientation":"0"}" data-image-title="uk_17_jan_2021_c-1" data-large-file="https://bskiesresearch.files.wordpress.com/2021/01/uk_17_jan_2021_c-1.png?w=700" data-link="https://bskiesresearch.wordpress.com/uk_17_jan_2021_c-1/" data-medium-file="https://bskiesresearch.files.wordpress.com/2021/01/uk_17_jan_2021_c-1.png?w=300" data-orig-file="https://bskiesresearch.files.wordpress.com/2021/01/uk_17_jan_2021_c-1.png" data-orig-size="1102,681" data-permalink="https://bskiesresearch.wordpress.com/uk_17_jan_2021_c-1/" data-url="https://bskiesresearch.files.wordpress.com/2021/01/uk_17_jan_2021_c-1.png" data-width="1102" height="247" src="https://bskiesresearch.files.wordpress.com/2021/01/uk_17_jan_2021_c-1.png" srcset="https://bskiesresearch.files.wordpress.com/2021/01/uk_17_jan_2021_c-1.png?strip=info&w=600 600w,https://bskiesresearch.files.wordpress.com/2021/01/uk_17_jan_2021_c-1.png?strip=info&w=681 681w" width="400" /></figure></div><div class="tiled-gallery__col" data-carousel-extra="{"blog_id":60752427,"permalink":"https:\/\/bskiesresearch.wordpress.com\/2021\/01\/18\/so-near-and-yet-not-quite\/"}" style="flex-basis: 50%;"><figure class="tiled-gallery__item"><img alt="" data-attachment-id="1808" data-comments-opened="1" data-height="681" data-id="1808" data-image-description="" data-image-meta="{"aperture":"0","credit":"","camera":"","caption":"","created_timestamp":"0","copyright":"","focal_length":"0","iso":"0","shutter_speed":"0","title":"","orientation":"0"}" data-image-title="uk_17_jan_2021_d-1" data-large-file="https://bskiesresearch.files.wordpress.com/2021/01/uk_17_jan_2021_d-1.png?w=700" data-link="https://bskiesresearch.wordpress.com/uk_17_jan_2021_d-1/" data-medium-file="https://bskiesresearch.files.wordpress.com/2021/01/uk_17_jan_2021_d-1.png?w=300" data-orig-file="https://bskiesresearch.files.wordpress.com/2021/01/uk_17_jan_2021_d-1.png" data-orig-size="1102,681" data-permalink="https://bskiesresearch.wordpress.com/uk_17_jan_2021_d-1/" data-url="https://bskiesresearch.files.wordpress.com/2021/01/uk_17_jan_2021_d-1.png" data-width="1102" height="247" src="https://bskiesresearch.files.wordpress.com/2021/01/uk_17_jan_2021_d-1.png" srcset="https://bskiesresearch.files.wordpress.com/2021/01/uk_17_jan_2021_d-1.png?strip=info&w=600 600w,https://bskiesresearch.files.wordpress.com/2021/01/uk_17_jan_2021_d-1.png?strip=info&w=681 681w" width="400" /></figure></div></div></div></div> <p class="has-text-align-justify">And here is the resulting median projection for total cumulative infections and deaths as a direct comparison to the previous blog post:</p> <div class="wp-block-jetpack-tiled-gallery aligncenter is-style-rectangular" data-carousel-extra="{"blog_id":60752427,"permalink":"https:\/\/bskiesresearch.wordpress.com\/2021\/01\/18\/so-near-and-yet-not-quite\/"}"><div class="tiled-gallery__gallery" data-carousel-extra="{"blog_id":60752427,"permalink":"https:\/\/bskiesresearch.wordpress.com\/2021\/01\/18\/so-near-and-yet-not-quite\/"}"><div class="tiled-gallery__row" data-carousel-extra="{"blog_id":60752427,"permalink":"https:\/\/bskiesresearch.wordpress.com\/2021\/01\/18\/so-near-and-yet-not-quite\/"}"><div class="tiled-gallery__col" data-carousel-extra="{"blog_id":60752427,"permalink":"https:\/\/bskiesresearch.wordpress.com\/2021\/01\/18\/so-near-and-yet-not-quite\/"}" style="flex-basis: 50%;"><figure class="tiled-gallery__item"><img alt="" data-attachment-id="1788" data-comments-opened="1" data-height="681" data-id="1788" data-image-description="" data-image-meta="{"aperture":"0","credit":"","camera":"","caption":"","created_timestamp":"0","copyright":"","focal_length":"0","iso":"0","shutter_speed":"0","title":"","orientation":"0"}" data-image-title="total_inf_18_jan_2021-1" data-large-file="https://bskiesresearch.files.wordpress.com/2021/01/total_inf_18_jan_2021-1.png?w=700" data-link="https://bskiesresearch.wordpress.com/total_inf_18_jan_2021-1/" data-medium-file="https://bskiesresearch.files.wordpress.com/2021/01/total_inf_18_jan_2021-1.png?w=300" data-orig-file="https://bskiesresearch.files.wordpress.com/2021/01/total_inf_18_jan_2021-1.png" data-orig-size="1102,681" data-permalink="https://bskiesresearch.wordpress.com/total_inf_18_jan_2021-1/" data-url="https://bskiesresearch.files.wordpress.com/2021/01/total_inf_18_jan_2021-1.png" data-width="1102" height="247" src="https://bskiesresearch.files.wordpress.com/2021/01/total_inf_18_jan_2021-1.png" srcset="https://bskiesresearch.files.wordpress.com/2021/01/total_inf_18_jan_2021-1.png?strip=info&w=600 600w,https://bskiesresearch.files.wordpress.com/2021/01/total_inf_18_jan_2021-1.png?strip=info&w=681 681w" width="400" /></figure></div><div class="tiled-gallery__col" data-carousel-extra="{"blog_id":60752427,"permalink":"https:\/\/bskiesresearch.wordpress.com\/2021\/01\/18\/so-near-and-yet-not-quite\/"}" style="flex-basis: 50%;"><figure class="tiled-gallery__item"><img alt="" data-attachment-id="1789" data-comments-opened="1" data-height="681" data-id="1789" data-image-description="" data-image-meta="{"aperture":"0","credit":"","camera":"","caption":"","created_timestamp":"0","copyright":"","focal_length":"0","iso":"0","shutter_speed":"0","title":"","orientation":"0"}" data-image-title="total_death_18_jan_2021" data-large-file="https://bskiesresearch.files.wordpress.com/2021/01/total_death_18_jan_2021.png?w=700" data-link="https://bskiesresearch.wordpress.com/total_death_18_jan_2021/" data-medium-file="https://bskiesresearch.files.wordpress.com/2021/01/total_death_18_jan_2021.png?w=300" data-orig-file="https://bskiesresearch.files.wordpress.com/2021/01/total_death_18_jan_2021.png" data-orig-size="1102,681" data-permalink="https://bskiesresearch.wordpress.com/total_death_18_jan_2021/" data-url="https://bskiesresearch.files.wordpress.com/2021/01/total_death_18_jan_2021.png" data-width="1102" height="247" src="https://bskiesresearch.files.wordpress.com/2021/01/total_death_18_jan_2021.png" srcset="https://bskiesresearch.files.wordpress.com/2021/01/total_death_18_jan_2021.png?strip=info&w=600 600w,https://bskiesresearch.files.wordpress.com/2021/01/total_death_18_jan_2021.png?strip=info&w=681 681w" width="400" /></figure></div></div></div></div> <p class="has-text-align-justify">It’s a remarkable turnaround, and looks like we are on track for about 114-86 = 28k additional deaths (to start of April), which is far lower than looked possible a couple of weeks ago. It seems plausible that an large part of the reason for the striking success of the suppression is that the transmission of the new variant was predominantly enhanced in the young and therefore closing schools has had a particularly strong effect. The assumption that lockdown lasts for 6 weeks, and what happens after it, is entirely speculative on my part but I wanted to test how close we were to herd immunity at that point. Clearly there will be more work to be done at that time but it shouldn’t be so devastating as at present, unless we lose all our immunity very rapidly.</p> <p class="has-text-align-justify">So that’s looking much better than it was. However it’s also interesting to think about what might have happened if the Govt had introduced the current restrictions sooner. Moving the start of the lockdown back by three weeks generates the following epidemic trajectory:</p> <div class="wp-block-jetpack-tiled-gallery aligncenter is-style-rectangular" data-carousel-extra="{"blog_id":60752427,"permalink":"https:\/\/bskiesresearch.wordpress.com\/2021\/01\/18\/so-near-and-yet-not-quite\/"}"><div class="tiled-gallery__gallery" data-carousel-extra="{"blog_id":60752427,"permalink":"https:\/\/bskiesresearch.wordpress.com\/2021\/01\/18\/so-near-and-yet-not-quite\/"}"><div class="tiled-gallery__row" data-carousel-extra="{"blog_id":60752427,"permalink":"https:\/\/bskiesresearch.wordpress.com\/2021\/01\/18\/so-near-and-yet-not-quite\/"}"><div class="tiled-gallery__col" data-carousel-extra="{"blog_id":60752427,"permalink":"https:\/\/bskiesresearch.wordpress.com\/2021\/01\/18\/so-near-and-yet-not-quite\/"}" style="flex-basis: 50%;"><figure class="tiled-gallery__item"><img alt="" data-attachment-id="1792" data-comments-opened="1" data-height="681" data-id="1792" data-image-description="" data-image-meta="{"aperture":"0","credit":"","camera":"","caption":"","created_timestamp":"0","copyright":"","focal_length":"0","iso":"0","shutter_speed":"0","title":"","orientation":"0"}" data-image-title="uk_17_jan_2021_c_no_christmas" data-large-file="https://bskiesresearch.files.wordpress.com/2021/01/uk_17_jan_2021_c_no_christmas.png?w=700" data-link="https://bskiesresearch.wordpress.com/uk_17_jan_2021_c_no_christmas/" data-medium-file="https://bskiesresearch.files.wordpress.com/2021/01/uk_17_jan_2021_c_no_christmas.png?w=300" data-orig-file="https://bskiesresearch.files.wordpress.com/2021/01/uk_17_jan_2021_c_no_christmas.png" data-orig-size="1102,681" data-permalink="https://bskiesresearch.wordpress.com/uk_17_jan_2021_c_no_christmas/" data-url="https://bskiesresearch.files.wordpress.com/2021/01/uk_17_jan_2021_c_no_christmas.png" data-width="1102" height="247" src="https://bskiesresearch.files.wordpress.com/2021/01/uk_17_jan_2021_c_no_christmas.png" srcset="https://bskiesresearch.files.wordpress.com/2021/01/uk_17_jan_2021_c_no_christmas.png?strip=info&w=600 600w,https://bskiesresearch.files.wordpress.com/2021/01/uk_17_jan_2021_c_no_christmas.png?strip=info&w=681 681w" width="400" /></figure></div><div class="tiled-gallery__col" data-carousel-extra="{"blog_id":60752427,"permalink":"https:\/\/bskiesresearch.wordpress.com\/2021\/01\/18\/so-near-and-yet-not-quite\/"}" style="flex-basis: 50%;"><figure class="tiled-gallery__item"><img alt="" data-attachment-id="1793" data-comments-opened="1" data-height="681" data-id="1793" data-image-description="" data-image-meta="{"aperture":"0","credit":"","camera":"","caption":"","created_timestamp":"0","copyright":"","focal_length":"0","iso":"0","shutter_speed":"0","title":"","orientation":"0"}" data-image-title="uk_17_jan_2021_d_no_christmas" data-large-file="https://bskiesresearch.files.wordpress.com/2021/01/uk_17_jan_2021_d_no_christmas.png?w=700" data-link="https://bskiesresearch.wordpress.com/uk_17_jan_2021_d_no_christmas/" data-medium-file="https://bskiesresearch.files.wordpress.com/2021/01/uk_17_jan_2021_d_no_christmas.png?w=300" data-orig-file="https://bskiesresearch.files.wordpress.com/2021/01/uk_17_jan_2021_d_no_christmas.png" data-orig-size="1102,681" data-permalink="https://bskiesresearch.wordpress.com/uk_17_jan_2021_d_no_christmas/" data-url="https://bskiesresearch.files.wordpress.com/2021/01/uk_17_jan_2021_d_no_christmas.png" data-width="1102" height="247" src="https://bskiesresearch.files.wordpress.com/2021/01/uk_17_jan_2021_d_no_christmas.png" srcset="https://bskiesresearch.files.wordpress.com/2021/01/uk_17_jan_2021_d_no_christmas.png?strip=info&w=600 600w,https://bskiesresearch.files.wordpress.com/2021/01/uk_17_jan_2021_d_no_christmas.png?strip=info&w=681 681w" width="400" /></figure></div></div></div></div> <p>and the resulting cumulative infections and deaths look like:</p> <div class="wp-block-jetpack-tiled-gallery aligncenter is-style-rectangular" data-carousel-extra="{"blog_id":60752427,"permalink":"https:\/\/bskiesresearch.wordpress.com\/2021\/01\/18\/so-near-and-yet-not-quite\/"}"><div class="tiled-gallery__gallery" data-carousel-extra="{"blog_id":60752427,"permalink":"https:\/\/bskiesresearch.wordpress.com\/2021\/01\/18\/so-near-and-yet-not-quite\/"}"><div class="tiled-gallery__row" data-carousel-extra="{"blog_id":60752427,"permalink":"https:\/\/bskiesresearch.wordpress.com\/2021\/01\/18\/so-near-and-yet-not-quite\/"}"><div class="tiled-gallery__col" data-carousel-extra="{"blog_id":60752427,"permalink":"https:\/\/bskiesresearch.wordpress.com\/2021\/01\/18\/so-near-and-yet-not-quite\/"}" style="flex-basis: 50%;"><figure class="tiled-gallery__item"><img alt="" data-attachment-id="1795" data-comments-opened="1" data-height="681" data-id="1795" data-image-description="" data-image-meta="{"aperture":"0","credit":"","camera":"","caption":"","created_timestamp":"0","copyright":"","focal_length":"0","iso":"0","shutter_speed":"0","title":"","orientation":"0"}" data-image-title="total_inf_early_18_jan_2021-1" data-large-file="https://bskiesresearch.files.wordpress.com/2021/01/total_inf_early_18_jan_2021-1.png?w=700" data-link="https://bskiesresearch.wordpress.com/total_inf_early_18_jan_2021-1/" data-medium-file="https://bskiesresearch.files.wordpress.com/2021/01/total_inf_early_18_jan_2021-1.png?w=300" data-orig-file="https://bskiesresearch.files.wordpress.com/2021/01/total_inf_early_18_jan_2021-1.png" data-orig-size="1102,681" data-permalink="https://bskiesresearch.wordpress.com/total_inf_early_18_jan_2021-1/" data-url="https://bskiesresearch.files.wordpress.com/2021/01/total_inf_early_18_jan_2021-1.png" data-width="1102" height="247" src="https://bskiesresearch.files.wordpress.com/2021/01/total_inf_early_18_jan_2021-1.png" srcset="https://bskiesresearch.files.wordpress.com/2021/01/total_inf_early_18_jan_2021-1.png?strip=info&w=600 600w,https://bskiesresearch.files.wordpress.com/2021/01/total_inf_early_18_jan_2021-1.png?strip=info&w=681 681w" width="400" /></figure></div><div class="tiled-gallery__col" data-carousel-extra="{"blog_id":60752427,"permalink":"https:\/\/bskiesresearch.wordpress.com\/2021\/01\/18\/so-near-and-yet-not-quite\/"}" style="flex-basis: 50%;"><figure class="tiled-gallery__item"><img alt="" data-attachment-id="1796" data-comments-opened="1" data-height="681" data-id="1796" data-image-description="" data-image-meta="{"aperture":"0","credit":"","camera":"","caption":"","created_timestamp":"0","copyright":"","focal_length":"0","iso":"0","shutter_speed":"0","title":"","orientation":"0"}" data-image-title="total_death_early_18_jan_2021" data-large-file="https://bskiesresearch.files.wordpress.com/2021/01/total_death_early_18_jan_2021.png?w=700" data-link="https://bskiesresearch.wordpress.com/total_death_early_18_jan_2021/" data-medium-file="https://bskiesresearch.files.wordpress.com/2021/01/total_death_early_18_jan_2021.png?w=300" data-orig-file="https://bskiesresearch.files.wordpress.com/2021/01/total_death_early_18_jan_2021.png" data-orig-size="1102,681" data-permalink="https://bskiesresearch.wordpress.com/total_death_early_18_jan_2021/" data-url="https://bskiesresearch.files.wordpress.com/2021/01/total_death_early_18_jan_2021.png" data-width="1102" height="247" src="https://bskiesresearch.files.wordpress.com/2021/01/total_death_early_18_jan_2021.png" srcset="https://bskiesresearch.files.wordpress.com/2021/01/total_death_early_18_jan_2021.png?strip=info&w=600 600w,https://bskiesresearch.files.wordpress.com/2021/01/total_death_early_18_jan_2021.png?strip=info&w=681 681w" width="400" /></figure></div></div></div></div> <p class="has-text-align-justify">Due to the automatic placing of text it’s not so easy to read but we end up with about 84000 deaths total (to end of March) which is fewer than we’ve already had.</p> <p>So the additional 30k deaths seems to be the price we paid for Johnson’s determination to battle the experts and save Christmas.</p> <figure class="wp-block-embed is-type-rich is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio"><div class="wp-block-embed__wrapper" data-carousel-extra="{"blog_id":60752427,"permalink":"https:\/\/bskiesresearch.wordpress.com\/2021\/01\/18\/so-near-and-yet-not-quite\/"}"> <iframe allowfullscreen="true" class="youtube-player" height="394" sandbox="allow-scripts allow-same-origin allow-popups allow-presentation" src="https://www.youtube.com/embed/hiKuxfcSrEU?version=3&rel=1&showsearch=0&showinfo=1&iv_load_policy=1&fs=1&hl=en&autohide=2&wmode=transparent" style="border: 0;" width="700"></iframe> </div></figure> James Annanhttp://www.blogger.com/profile/04318741813895533700noreply@blogger.com3tag:blogger.com,1999:blog-9959776.post-10010089401377384712021-01-07T12:36:00.002+00:002021-01-13T07:38:10.451+00:00BlueSkiesResearch.org.uk: Not even half-way there <p class="has-text-align-justify" style="text-align: justify;">NB: below calculation was made and published on Monday 4th, when schools had just been opened and before the latest lockdown was announced, so we can hope that it is too pessimistic, but the situation is still very challenging.</p><hr /><p class="has-text-align-justify" style="text-align: justify;">Lots of talk from politicians and others that, while not exactly triumphalist, is certainly very positive and enthusiastic about the prospect of vaccinating ourselves out of trouble. <a href="https://www.bbc.co.uk/news/uk-northern-ireland-55172043">Here’s one of the earliest "light at the end of the tunnel" articles</a> for example. And with the <a href="https://www.bbc.co.uk/news/uk-55525542">new Oxford/AZ vaccine</a> there is renewed excitement.</p> <p class="has-text-align-justify" style="text-align: justify;">Sorry to pour a little bit of cold water on the mood but a bit of perspective is called for.</p> <p class="has-text-align-justify" style="text-align: justify;">Here is what my modelling suggests for the progress of the outbreak though the population so far and into the future. It’s not a pretty sight. The total number that may be infected between now and the start of March (less than 2 months away) is more than the entire number that have been infected so far right from the start of the outbreak last Feb/March.</p> <figure class="wp-block-image size-large"><a href="https://bskiesresearch.files.wordpress.com/2021/01/total_inf_03_jan_2021-1.png"><img alt="" class="wp-image-1777" data-attachment-id="1777" data-comments-opened="1" data-image-description="" data-image-meta="{"aperture":"0","credit":"","camera":"","caption":"","created_timestamp":"0","copyright":"","focal_length":"0","iso":"0","shutter_speed":"0","title":"","orientation":"0"}" data-image-title="total_inf_03_jan_2021-1" data-large-file="https://bskiesresearch.files.wordpress.com/2021/01/total_inf_03_jan_2021-1.png?w=700" data-medium-file="https://bskiesresearch.files.wordpress.com/2021/01/total_inf_03_jan_2021-1.png?w=300" data-orig-file="https://bskiesresearch.files.wordpress.com/2021/01/total_inf_03_jan_2021-1.png" data-orig-size="1254,775" data-permalink="https://bskiesresearch.wordpress.com/total_inf_03_jan_2021-1/" height="395" sizes="(max-width: 1024px) 100vw, 1024px" src="https://bskiesresearch.files.wordpress.com/2021/01/total_inf_03_jan_2021-1.png?w=1024" srcset="https://bskiesresearch.files.wordpress.com/2021/01/total_inf_03_jan_2021-1.png?w=1024 1024w, https://bskiesresearch.files.wordpress.com/2021/01/total_inf_03_jan_2021-1.png?w=150 150w, https://bskiesresearch.files.wordpress.com/2021/01/total_inf_03_jan_2021-1.png?w=300 300w, https://bskiesresearch.files.wordpress.com/2021/01/total_inf_03_jan_2021-1.png?w=768 768w, https://bskiesresearch.files.wordpress.com/2021/01/total_inf_03_jan_2021-1.png 1254w" width="640" /></a></figure> <p class="has-text-align-justify" style="text-align: justify;">According to these calculations, roughly 15 million have been infected, and a total of roughly 36 million may be by the time it’s over. That is, we have significantly more infections to come, than we have seen so far. And far more than we got in the first wave last spring, when probably something like 10% (my modelling actually says 8%) of the population was infected.</p> <p style="text-align: justify;"><em>If there ever was a time to stay at home and minimise all unnecessary contact, it most surely is now.</em></p> <p class="has-text-align-justify" style="text-align: justify;">With this rate of spread, vaccinating a few million over the next couple of months has a relatively minor effect. It may reduce the death rate significantly towards the end of this period (and will certainly help the small minority of highly vulnerable people who receive it), but won’t stop the disease spreading widely.</p> <p class="has-text-align-justify" style="text-align: justify;">I need to add a few disclaimers about the modelling. This result plotted above is the median of my latest ensemble fit of a simple SEIR model to historical data on deaths and cases. I’ve been modelling the progress of the outbreak for months now and though the model is rather primitive and approximate it has done a pretty decent job of simulating what is actually quite a simple process. If each infected person passes the disease on to more than one other (on average), then the disease grows exponentially, if they pass it on to less than one (on average) then it shrinks exponentially. The more difficult bits (that my model is too simple to attempt) is to predict the effect of specific restrictions such as closing schools or pubs, or determining how many young vs old people get ill. When just looking at total numbers, this simple SEIR model (when carefully used) works better than it probably should.</p> <p class="has-text-align-justify" style="text-align: justify;">This simulation, while it fits the historical data well, may not account adequately for the added virulence of the newer strain that has recently emerged. It also assumes that we don’t have an extremely strict lockdown that successfully suppresses the outbreak in the very near future. Reality could end up better than this, or it could end up worse, but I’m pretty confident that the basic message is robust. People are getting infected at a huge rate right now. Stay at home if you can.</p> James Annanhttp://www.blogger.com/profile/04318741813895533700noreply@blogger.com0tag:blogger.com,1999:blog-9959776.post-69392243164766428942020-12-22T15:29:00.004+00:002020-12-22T19:22:04.296+00:00The new variant<p style="text-align: justify;">The summary is, yes it's real, yes it's serious, and the early signs are that it could be very difficult to maintain any semblance of suppression in the next month or two. Vulnerable people would be well advised to put off and/or cut down any risky activities at least for now, especially with vaccination just around the corner. It's not necessarily any worse if you catch it, but it is spreading rapidly and will be much more likely to infect you. The one glimmer of good news is that the vaccination seems to be progressing smoothly and at a decent pace, though obviously the sooner we can get more supplies of them, the better.</p><hr style="text-align: justify;" /><p style="text-align: justify;">When the new variant was announced last week, I assumed (along with many others, I think) that its impact was probably exaggerated to cover up the govt's embarrassment over the Christmas U-turn. It was only a couple of days previously that Johnson had derided Starmer for suggesting that the Plaguefest plans should be reconsidered. Starmer had been the Grinch that wanted to Cancel Christmas! And now....it was Johnson doing the cancelling. Such is the effect of the torrent of lies and excuses and u-turns that we've been subjected to over recent months and even years. But....there <i>is</i> a new variant, and it <i>is</i> growing.</p><p style="text-align: justify;">It has been traced back to September - one thing the UK actually can legitimately claim to be good at is genetic sequencing a sizeable proportion of samples - and has been getting more and more common since then. <a href="https://www.ecdc.europa.eu/sites/default/files/documents/SARS-CoV-2-variant-multiple-spike-protein-mutations-United-Kingdom.pdf">Here's</a> an assessment from the ECDC on the 20th Dec. The blue line on this figure shows the proportion of samples containing the new variant, over several weeks (right hand scale).</p><div class="separator" style="clear: both; text-align: justify;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEit2sAHduyclFFSzj4eENp_xR7jmrS5edplpLb_HIra9krDCtg3dopKb0m2h8hJ1d6oU1tg0Ck3vZZrI0g5bZFAr6qxhKwPym4D8enzH2FYUuL43pg-NX9GTGOfUJv1NntkiG8/s1660/Screen+Shot+2020-12-22+at+14.05.31.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1076" data-original-width="1660" height="414" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEit2sAHduyclFFSzj4eENp_xR7jmrS5edplpLb_HIra9krDCtg3dopKb0m2h8hJ1d6oU1tg0Ck3vZZrI0g5bZFAr6qxhKwPym4D8enzH2FYUuL43pg-NX9GTGOfUJv1NntkiG8/w640-h414/Screen+Shot+2020-12-22+at+14.05.31.png" width="640" /></a></div><div style="text-align: justify;"><br /></div><p style="text-align: justify;">It's been doubling every week over the second half of this period, a little quicker than that in fact. This isn't itself enough to tell us how fast is is growing in absolute terms, but the total number of positive cases was fairly flat over the relevant portion of this interval, maybe declining a little at the very end (the last week, number 47, is <a href="https://www.epochconverter.com/weeks/2020">probably around 16-22 Nov</a>). So that means it's close to doubling every week in absolute terms, which would work out at an R number of about 1.7, over a period of lockdown when the underlying R number for general infections was close to 1. Another set of data generates a somewhat lower estimate, but it's still clearly higher for the new variant than the old one:</p><div class="separator" style="clear: both; text-align: justify;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEghhvxXcDL8micLHjXJnKl5CoVZ2cTSUcl-yR66kAu8V9l2Uo7Vr1DluLywdAH6nyYRpoxyesytrFfKYxi3LEYwqJ5tztogjwNMktSiodkZcdabHffQoE8n1aMKhWml1Q8QeZA/s965/EpnSfEjXEAA-e9l.jpeg" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="664" data-original-width="965" height="440" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEghhvxXcDL8micLHjXJnKl5CoVZ2cTSUcl-yR66kAu8V9l2Uo7Vr1DluLywdAH6nyYRpoxyesytrFfKYxi3LEYwqJ5tztogjwNMktSiodkZcdabHffQoE8n1aMKhWml1Q8QeZA/w640-h440/EpnSfEjXEAA-e9l.jpeg" width="640" /></a></div><div style="text-align: justify;"><br /></div><p style="text-align: justify;">The proportion of new variant roughly doubled in three weeks, but the total number of new cases was also well up over this period, meaning that the absolute growth rate for the new variant was faster than this.</p><p style="text-align: justify;">A <a href="https://assets.publishing.service.gov.uk/government/uploads/system/uploads/attachment_data/file/947048/Technical_Briefing_VOC_SH_NJL2_SH2.pdf">more comprehensive analysis</a> was published last night by PHE and this is the key figure:</p><p style="text-align: justify;"><br /></p><div class="separator" style="clear: both; text-align: justify;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgcH1cVnVNvDcZWyQol9fMo6lBQo4uM29rp_r5rwUwRSBbX7S3_-x7t7IOroLgkbLSFjuV_IauAvlOlXxCJCza74R_CKmVYPC4n-G0ZVYCth8bxNFQn3-yEDhyWtbxNRvz5qxU/s1368/Screen+Shot+2020-12-22+at+14.37.44.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="864" data-original-width="1368" height="404" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgcH1cVnVNvDcZWyQol9fMo6lBQo4uM29rp_r5rwUwRSBbX7S3_-x7t7IOroLgkbLSFjuV_IauAvlOlXxCJCza74R_CKmVYPC4n-G0ZVYCth8bxNFQn3-yEDhyWtbxNRvz5qxU/w640-h404/Screen+Shot+2020-12-22+at+14.37.44.png" width="640" /></a></div><div style="text-align: justify;"><br /></div><p style="text-align: justify;">Each dot is the ratio of weekly growth rates for the new variant versus older type, over several weeks (colour coded) and different regions. The blue line is a fitted mean and it's clearly above 1. The scale is supposed to represent the ratio of R numbers for the two variants and they have made a slightly embarrassing error on this calculation which they may excuse as a reasonable approximation though there's no real reason to have done it as it's not really much harder to have done it correctly. It doesn't really matter so long as no-one considers the numerical result to be some precise truth. The point is that the new variant has a substantially larger growth rate, sufficient for case numbers to have actually been rising in absolute numbers during the latter part of the last "lockdown" in London. They get a typical advantage of about 0.5 in additive terms, or you could call it 1.7 as a multiplicative factor (these data mostly relate to during lockdown when R<1 was a reasonable assumption for the old variant). How the different R numbers relate may depend in part on the background restriction in place, it's not something really amenable to precision.</p><p style="text-align: justify;">So the exact answer is uncertain, but it's quite plausible that the R number for this new variant could currently be as high as 1.5 now nationally or even higher, which suggests that it might be very hard to get it below 1 on any sort of sustainable basis. We certainly have a race against time to get as far through the vaccination list as quickly as possible. <a href="https://www.omnicalculator.com/health/vaccine-queue-uk">This calculator</a> suggests that a 70 year old person with no additional health conditions might get vaccinated as early as Feb (though the estimate of 1 million per week is surely a bit of a guess). 80 year olds by late Jan. Even getting that far could cut total deaths in half:</p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEguHKZmnI2ebSTO7QOf04sHst6G11TAERt8VoKSG-QFI3sl_z2ZuiqP94ckLZYnmwVah8XE7er_GK4w-9WKVyUmN6jRtZFwxl115yU1IQa0X5BONXl9N4HZa6YPq_hzI6XIh4o/s1125/EpMWhxmXIAEwrPV.jpeg" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="625" data-original-width="1125" height="356" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEguHKZmnI2ebSTO7QOf04sHst6G11TAERt8VoKSG-QFI3sl_z2ZuiqP94ckLZYnmwVah8XE7er_GK4w-9WKVyUmN6jRtZFwxl115yU1IQa0X5BONXl9N4HZa6YPq_hzI6XIh4o/w640-h356/EpMWhxmXIAEwrPV.jpeg" width="640" /></a></div><br /><p style="text-align: justify;">(from <a href="https://twitter.com/ActuaryByDay/status/1338438288592482306?s=20">ActuaryByDay</a> who is pretty reliable though this figure assumes 100% effectiveness which is obviously a generous estimate, scaling the values by 0.9 to account for this would be an improvement and maybe another 0.8(??) to account for incomplete take-up.)</p><p style="text-align: justify;">While we roll out the vaccine, it's surely worth re-emphasising the one obvious lesson of the last 9 months - that it's better to act quickly than to hope in vain that it's all going to turn out fine. If this new variant turns out to be anywhere near as bad as these data suggest, we should be acting with extreme urgency to buy ourselves as much time as possible. If it turns out to not be as bad as I'm suggesting, we can drop the restrictions quickly and the additional harm will be modest. Evidence is coming in quickly but the cost of delay is rising exponentially.</p>James Annanhttp://www.blogger.com/profile/04318741813895533700noreply@blogger.com2tag:blogger.com,1999:blog-9959776.post-85133218336636127172020-12-22T12:33:00.001+00:002020-12-22T12:33:15.466+00:00BlueSkiesResearch.org.uk: Science breakthrough of the year (runner-up) <p class="has-text-align-justify" style="text-align: justify;">Being only a small and insignificant organisation, we would like to take this rare opportunity to blow our own trumpets.</p> <p class="has-text-align-justify" style="text-align: justify;">Blue Skies Research contributed to <a href="https://vis.sciencemag.org/breakthrough2020/#/finalists/global-warming-forecasts-sharpen">one of the runners-up</a> in Science Magazine’s “<a href="https://vis.sciencemag.org/breakthrough2020/">Breakthrough of the year</a>” review! Specifically, the estimation of climate sensitivity that I previously <a href="https://bskiesresearch.wordpress.com/2020/07/22/back-to-the-future/">blogged about here</a>.</p> <p class="has-text-align-justify" style="text-align: justify;">Obviously, were it not for the pesky virus, we would have won outright.</p> James Annanhttp://www.blogger.com/profile/04318741813895533700noreply@blogger.com0tag:blogger.com,1999:blog-9959776.post-88498367106112936712020-11-09T06:44:00.000+00:002020-11-09T06:44:37.760+00:00BlueSkiesResearch.org.uk: Modelling the ONS COVID data<p class="has-text-align-justify">I’ve grumbled for a while about the <a href="https://www.ons.gov.uk/peoplepopulationandcommunity/healthandsocialcare/conditionsanddiseases/bulletins/coronaviruscovid19infectionsurveypilot/previousReleases">ONS analyses of their infection survey pilot</a> (pilot? isn’t it a full-blown survey yet?) without doing anything about it. The purpose of this blog is to outline the issue, get me started on fixing it (or at least presenting my own approach to an analysis) and commit me to actually doing it this time. There are a couple of minor obstacles that I’ve been using as an excuse for several weeks now and it’s time I had a go.</p> <p class="has-text-align-justify">The survey itself seems good – they are regularly testing a large "random" cohort of people for their infection status, and thereby estimating the prevalence of the disease and how it varies over time. The problem is in how they are doing this estimation. They are fitting a curve through their data, using a method know as a "<a href="https://en.wikipedia.org/wiki/Thin_plate_spline">thin plate spline</a>." I am not familiar with this approach but it’s essentially a generic smooth curve that attempts to minimise wiggles.</p> <p class="has-text-align-justify">There are two fundamental problems with their analysis, which may be related (or not) but are both important IMO. The first is that this smooth curve isn’t necessarily a credible epidemic curve. Epidemics have a particular dynamical form (you can think of them as locally exponential for the most part, though this is a bit of an oversimplification) and while variation in R over time gives rise to some flexibility in the outcome of this process, there are also inevitably constraints due to the way that infections arise and are detected. In short, the curve they are fitting has no theoretical foundation as the model of an epidemic. In practice it has often appeared to me that the curves have looked a bit unrealistic though of course I don’t claim to have much experience to draw on here!</p> <p class="has-text-align-justify">The second fundamental problem is the empirical observation that their analyses are inconsistent and incoherent. This is illustrated in the following analysis of their <a href="https://www.ons.gov.uk/peoplepopulationandcommunity/healthandsocialcare/conditionsanddiseases/bulletins/coronaviruscovid19infectionsurveypilot/englandandwales4september2020">Sept 4th results</a>:</p> <p><img alt="" class="wp-image-1709" data-attachment-id="1709" data-comments-opened="1" data-image-description="" data-image-meta="{"aperture":"0","credit":"","camera":"","caption":"","created_timestamp":"0","copyright":"","focal_length":"0","iso":"0","shutter_speed":"0","title":"","orientation":"0"}" data-image-title="Screen Shot 2020-11-08 at 11.05.22" data-large-file="https://bskiesresearch.files.wordpress.com/2020/11/screen-shot-2020-11-08-at-11.05.22.png?w=700" data-medium-file="https://bskiesresearch.files.wordpress.com/2020/11/screen-shot-2020-11-08-at-11.05.22.png?w=300" data-orig-file="https://bskiesresearch.files.wordpress.com/2020/11/screen-shot-2020-11-08-at-11.05.22.png" data-orig-size="1428,820" data-permalink="https://bskiesresearch.wordpress.com/2020/11/08/modelling-the-ons-covid-data/screen-shot-2020-11-08-at-11-05-22/" src="https://bskiesresearch.files.wordpress.com/2020/11/screen-shot-2020-11-08-at-11.05.22.png" style="width: 1000px;" /></p> <p class="has-text-align-justify">Here we see their on the right their model fit (plume) to the last few months of data (the data themselves are not shown). The dot and bar is their estimate for the final week which is one of the main outputs of their analysis. On the left, we see the equivalent latest-week estimates from previous reports which have been produced at roughly weekly intervals The last dot and bar is a duplicate of the one on the right hand panel. It is straightforward to superimpose these graphics thusly:</p> <figure class="wp-block-image size-large"><a href="https://bskiesresearch.files.wordpress.com/2020/11/ehejd6ewoaer04f.png"><img alt="" class="wp-image-1712" data-attachment-id="1712" data-comments-opened="1" data-image-description="" data-image-meta="{"aperture":"0","credit":"","camera":"","caption":"","created_timestamp":"0","copyright":"","focal_length":"0","iso":"0","shutter_speed":"0","title":"","orientation":"0"}" data-image-title="ehejd6ewoaer04f" data-large-file="https://bskiesresearch.files.wordpress.com/2020/11/ehejd6ewoaer04f.png?w=680" data-medium-file="https://bskiesresearch.files.wordpress.com/2020/11/ehejd6ewoaer04f.png?w=300" data-orig-file="https://bskiesresearch.files.wordpress.com/2020/11/ehejd6ewoaer04f.png" data-orig-size="680,500" data-permalink="https://bskiesresearch.wordpress.com/ehejd6ewoaer04f/" sizes="(max-width: 680px) 100vw, 680px" src="https://bskiesresearch.files.wordpress.com/2020/11/ehejd6ewoaer04f.png?w=680" srcset="https://bskiesresearch.files.wordpress.com/2020/11/ehejd6ewoaer04f.png 680w, https://bskiesresearch.files.wordpress.com/2020/11/ehejd6ewoaer04f.png?w=150 150w, https://bskiesresearch.files.wordpress.com/2020/11/ehejd6ewoaer04f.png?w=300 300w" /></a></figure> <p class="has-text-align-justify">The issue here is that (for example) their dot and bar estimate several reports back centred on the 3rd August, has no overlap with their new plume. Both of these are supposed to be 95% intervals, meaning they are both claimed to have a 95% chance of including the real value. At least one of them does not.</p> <p class="has-text-align-justify">While it’s entirely to be expected that some 95% intervals will not contain reality, this should be rare, occurring only 5% of the time. Three of the dot and bar estimates in the above graphic are wholly disjoint with the plume, one more has negligible overlap and another two are in substantial disagreement. This is not just bad luck, it’s bad calibration. This phenomenon has continued subsequent to my observation, eg this is the equivalent from the 9th Oct:</p> <figure class="wp-block-image size-large"><a href="https://bskiesresearch.files.wordpress.com/2020/11/ej4oqg6xyaawocg.png"><img alt="" class="wp-image-1714" data-attachment-id="1714" data-comments-opened="1" data-image-description="" data-image-meta="{"aperture":"0","credit":"","camera":"","caption":"","created_timestamp":"0","copyright":"","focal_length":"0","iso":"0","shutter_speed":"0","title":"","orientation":"0"}" data-image-title="ej4oqg6xyaawocg" data-large-file="https://bskiesresearch.files.wordpress.com/2020/11/ej4oqg6xyaawocg.png?w=700" data-medium-file="https://bskiesresearch.files.wordpress.com/2020/11/ej4oqg6xyaawocg.png?w=300" data-orig-file="https://bskiesresearch.files.wordpress.com/2020/11/ej4oqg6xyaawocg.png" data-orig-size="724,464" data-permalink="https://bskiesresearch.wordpress.com/ej4oqg6xyaawocg/" sizes="(max-width: 724px) 100vw, 724px" src="https://bskiesresearch.files.wordpress.com/2020/11/ej4oqg6xyaawocg.png?w=724" srcset="https://bskiesresearch.files.wordpress.com/2020/11/ej4oqg6xyaawocg.png 724w, https://bskiesresearch.files.wordpress.com/2020/11/ej4oqg6xyaawocg.png?w=150 150w, https://bskiesresearch.files.wordpress.com/2020/11/ej4oqg6xyaawocg.png?w=300 300w" /></a></figure> <p class="has-text-align-justify">The previous dot and bar from late Sept is again disjoint from the new plume, and the one just after the dotted line in mid-August looks to be right on the limit depending on graphical resolution. In the most recent reports have changed the scaling of the graphics to make this overlaying more difficult, but there is no suggestion that they have fixed the underlying methodological issues.</p> <p class="has-text-align-justify">The obvious solution to all this is to fit a model along the lines of my existing approach, using a standard Bayesian paradigm, and I propose to do just this. First, let’s look at the data. The spreadsheet that accompanies the report each week gives various numerical summaries of the data and the one that I think is most usable for my purposes is the weighted fortnightly means in Table 1d which take the raw infection numbers and adjust to represent the population more accurately (presumably, accounting for things like different age distributions in the sample vs the national population). Thanks to the weekly publication of these data, we can actually create a series of overlapping fortnightly means out of two consecutive reports and I’ve plotted such a set here:</p> <figure class="wp-block-image size-large"><a href="https://bskiesresearch.files.wordpress.com/2020/11/ons_data_7_nov.png"><img alt="" class="wp-image-1718" data-attachment-id="1718" data-comments-opened="1" data-image-description="" data-image-meta="{"aperture":"0","credit":"","camera":"","caption":"","created_timestamp":"0","copyright":"","focal_length":"0","iso":"0","shutter_speed":"0","title":"","orientation":"0"}" data-image-title="ons_data_7_nov" data-large-file="https://bskiesresearch.files.wordpress.com/2020/11/ons_data_7_nov.png?w=700" data-medium-file="https://bskiesresearch.files.wordpress.com/2020/11/ons_data_7_nov.png?w=300" data-orig-file="https://bskiesresearch.files.wordpress.com/2020/11/ons_data_7_nov.png" data-orig-size="1264,781" data-permalink="https://bskiesresearch.wordpress.com/ons_data_7_nov/" sizes="(max-width: 1024px) 100vw, 1024px" src="https://bskiesresearch.files.wordpress.com/2020/11/ons_data_7_nov.png?w=1024" srcset="https://bskiesresearch.files.wordpress.com/2020/11/ons_data_7_nov.png?w=1024 1024w, https://bskiesresearch.files.wordpress.com/2020/11/ons_data_7_nov.png?w=150 150w, https://bskiesresearch.files.wordpress.com/2020/11/ons_data_7_nov.png?w=300 300w, https://bskiesresearch.files.wordpress.com/2020/11/ons_data_7_nov.png?w=768 768w, https://bskiesresearch.files.wordpress.com/2020/11/ons_data_7_nov.png 1264w" /></a></figure> <p class="has-text-align-justify">It’s not quite the latest data, I’m not going to waste effort updating this throughout the process until I’ve got a working algorithm at which point the latest set can just slot in. The black circles here are the mean estimates, with the black bars representing the 95% intervals from the table.</p> <p class="has-text-align-justify">Now we get to the minor headaches that I’d been procrastinating over for a while. The black bars are not generally symmetric around the central points as they arise from a binomial (type) distribution. My methods (in common with many efficient approaches) require the likelihood P(obs|model) to be Gaussian. The issue here is easy illustrated with a simple example. Let’s say the observations on a given day contain 10 positives in 1000 samples. If the model predicts 5 positives in a sample of 1000, then it’s quite unlikely we would obtain 10: P(O=10|m=5) = 1.8%. However if the model predicts 15 positives, the chance of seeing 10 is rather larger: P(O=10|m=15) = 4.8%. So even though both model predictions are an equal distance from the observation, the latter has a higher likelihood. A Gaussian (of any given width) would assign equal likelihood to both 5 and 15 as the observations are equally far from either of these predictions. I’ve wondered about trying to build in a transformation from binomial to Gaussian but for the first draft I’ll just use a Gaussian approximation which is shown in the plot as the symmetric red error bars. You can see a couple of them actually coincide with the black bars, presumably due to rounding on the data as presented in the table. The ones that don’t, are all biased slightly low relative to the consistent positive skew of the binomial. The skew in these data is rather small compared to that of my simple example but using the Gaussian approximation will result in all of my estimates being just a fraction low compared to the correct answer.</p> <p class="has-text-align-justify">Another issue is that the underlying sample data contribute to two consecutive fortnightly means in these summaries. A simple heuristic to account for this double-counting is to increase uncertainties by a factor sqrt(2) as shown by the blue bars. This isn’t formally correct and I may eventually use the appropriate covariance matrix for observational uncertainties instead, but it’s easier to set up and debug this way and I bet it won’t make a detectable difference to the answer as the model will impose strong serial correlation on this time scale anyway.</p> <p class="has-text-align-justify">So that’s how I’m going to approach the problem. Someone was previously asking for an introduction to how this Bayesian estimation process works anyway. The basic idea is that we have a prior distribution of parameters/inputs P(Φ) from which we can draw an ensemble of samples. In this case, our main uncertain input is a time series of R which I’m treating as Brownian motion with a random daily perturbation. For each sample of Φ, we can run the model simulation and work out how likely we would be to observe the values that have been seen, if the real world had been the model – ie P(Obs|Φ). Using these likelihood values as weights, the weighted ensemble is directly interpretable as the posterior P(Φ|Obs). That really is all there is to it. The difficulties are mostly in designing a computationally efficient algorithm as the approach I have described may need a vast ensemble to work accurately and is therefore sometimes far too slow and expensive to apply to interesting problems. For example, my iterative Kalman smoother doesn’t actually use this algorithm at all, but instead uses a far more efficient way of getting to the same answer. One limitation that it requires (as mentioned above) is that the likelihood has to be expressed in Gaussian form.</p> </div> James Annanhttp://www.blogger.com/profile/04318741813895533700noreply@blogger.com3tag:blogger.com,1999:blog-9959776.post-33660229966778340292020-09-15T16:31:00.000+01:002020-09-15T16:31:02.112+01:00SAGE versus reality<p style="text-align: justify;">Something I've been meaning to do for a while is look at how well the SAGE estimates of the growth rate of the epidemic have matched up to reality over the long term. For the last 3 months now, <a href="https://www.gov.uk/guidance/the-r-number-in-the-uk">SAGE have published a weekly estimate not only of R but also the daily growth rate</a>, which is actually a more directly interpretable number (as well as being provided to a higher degree of precision). What I have done is taken their estimate of daily growth rate and integrated it over time. And plotted this against the number of cases actually reported.</p><p style="text-align: justify;">Here we are:</p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh8JFK8t_uwWCWiaCYvbHR1JS-99VvccGe8w5hWBHeeHo8j0HUwFSNwq9Q2ar9QNWOEvf1eunfiLu7F9iy39hUFOS_Na7haCGkUWQyM5setWcqv80OWF8mmU08P8g2CBhSg8EA/s631/SAGE.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="450" data-original-width="631" height="456" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh8JFK8t_uwWCWiaCYvbHR1JS-99VvccGe8w5hWBHeeHo8j0HUwFSNwq9Q2ar9QNWOEvf1eunfiLu7F9iy39hUFOS_Na7haCGkUWQyM5setWcqv80OWF8mmU08P8g2CBhSg8EA/w640-h456/SAGE.png" width="640" /></a></div><div style="text-align: justify;">The solid blue line is the central estimate from SAGE, with the dashed lines calculated using the ends of the range they published each week. Red is the weekly mean number of cases over this time period, with this line scaled to start at the same place in week 1 (ending on Friday 19 June). Latest SAGE estimate in this plot is from Friday 11 Sept.</div><p style="text-align: justify;">Agreement was very good for the first few weeks, with case numbers going down at the rate described by SAGE of about 3% per day. But then the case numbers started to drift up in July...and SAGE continued to say the epidemic was getting smaller. Over the last few weeks the discrepancy has grown sharply. Note that the dashed lines assume the extreme edge of the range presented by SAGE, week after week - so this would require a consistent bias in their methodology, rather than just a bit of random uncertainty.</p><p style="text-align: justify;">Honesty compels me to point out that the comparison here is not completely fair, as the number of cases may not be a consistent estimate of the size of the outbreak. Some of the rise in cases may be due to increased testing. However the discrepancy between case numbers and the mean SAGE estimate is now a factor of 10 compared to the starting point of this analysis. That's not due to better testing alone!</p>James Annanhttp://www.blogger.com/profile/04318741813895533700noreply@blogger.com3tag:blogger.com,1999:blog-9959776.post-66228606751977347742020-09-12T17:53:00.006+01:002020-09-13T18:07:55.021+01:00Weekly RRRRRRReport<p style="text-align: justify;">A lot of different estimates of the growth rate (R) of the epidemic have come out in the last couple of days, so here's a summary of which ones are wrong (and why) and which ones you can believe. And who am I to do this, you might reasonably ask? While not an epidemiologist, my professional expertise is in fitting models to data, which is precisely what this question demands. And the available evidence suggests I'm rather better at it than many epidemiologists appear to be.</p><p style="text-align: justify;">As you may recall, a month ago <a href="https://julesandjames.blogspot.com/2020/08/could-r-still-be-less-than-1.html" target="_blank">I posted an argument</a> that R really couldn't be under 1 any longer, and the epidemic was starting to grow again. At the time, the "experts" of SAGE were still <a href="https://www.gov.uk/guidance/the-r-number-in-the-uk#full-history" target="_blank">insisting that R was less than 1</a>, and they kept on claiming that for a while, despite the very clear rise in reported case numbers. The rise has continued and indeed accelerated a bit, other than for a very brief hiatus in the middle of last month. Part of this steady rise might have be due to a bit more testing, but it's been pretty implausible to believe that all of it was for a while now. I'll come back to SAGE's ongoing incompetence later.</p><p style="text-align: justify;">I'll start with my own estimate which currently comes out at R= ~1.3. This is based on fitting a very simple model to both case and death data, which the model struggles to reconcile due to its simplicity. The average death rate (as a percentage of infected people) has dropped in recent weeks, thanks to mostly younger people being infected recently, and perhaps also helped by some improvements in treatment. I could try to account for this in the model but haven't got round to it. So it consistently undershoots the case numbers and overshoots deaths a bit, but I don't think this biases the estimate of R enough to really matter (precisely because the biases are fairly constant). Incidentally, the method I'm using for the estimation is an iterative version of an ensemble Kalman smoother, which is a technique I developed about 15 years ago for a different purpose. It's rather effective for this problem and clearly superior to anything that the epidemiologists are aware of. Ho hum.</p><p style="text-align: justify;">Here are my plots of the fit to cases (top) and deaths (bottom) along with the R number.</p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjYWRnFwo5BdFqCKfyLyETtrmsJhlVgtbpDlLFLpufpSAHoy0fMZrtzaH2ff_nPUB-4oZpyW5A7X8hCy5YbvChmHl08-20bcTMDmclmjFDWk5hy7hxbY8ERRcT487XRErRgs6Q/s1330/uk_11_sept_c.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="822" data-original-width="1330" height="310" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjYWRnFwo5BdFqCKfyLyETtrmsJhlVgtbpDlLFLpufpSAHoy0fMZrtzaH2ff_nPUB-4oZpyW5A7X8hCy5YbvChmHl08-20bcTMDmclmjFDWk5hy7hxbY8ERRcT487XRErRgs6Q/w500-h310/uk_11_sept_c.png" width="500" /></a></div><div style="text-align: justify;"><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjmf-wUr2AtUI6SAsjJlORoeehflhdxDOlqXuPYRKcfCSRhChLYI7mIGdVw5KcKaOHL4Wkoqqg3KGNAK4oKk_yvd_PBbhkseTnxf3wvs_5Bo39UpUG73zHVQYWLA5RSXUF0dOM/s1330/uk_11_sept_d.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="822" data-original-width="1330" height="310" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjmf-wUr2AtUI6SAsjJlORoeehflhdxDOlqXuPYRKcfCSRhChLYI7mIGdVw5KcKaOHL4Wkoqqg3KGNAK4oKk_yvd_PBbhkseTnxf3wvs_5Bo39UpUG73zHVQYWLA5RSXUF0dOM/w500-h310/uk_11_sept_d.png" width="500" /></a></div><div style="text-align: justify;">As pointed out, these graphs need better annotation. Top graph is modelled daily infections (blue plume), modelled daily cases (green plume with some blue lines sampled from the ensemble and the median shown as magenta) and case ascertainment ratio which is basically the ratio of these (red plume, RH scale). Reported case numbers are the red circles. Bottom graph is modelled deaths (green plume with lines again) with data as red circles. Red plume here is the effective R number (RH scale). R number and case ascertainment are the fundamental parameters that are being fitted in my approach. Infection fatality rate is fixed at 0.75%.</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">So far, so good. Well, bad, but hopefully you know what I mean.</div><p style="text-align: justify;">Another relevant weekly analysis that came out recently is the <a href="https://www.ons.gov.uk/peoplepopulationandcommunity/healthandsocialcare/conditionsanddiseases/bulletins/coronaviruscovid19infectionsurveypilot/11september2020" target="_blank">infection pilot survey from ONS</a>. Up to now it's been pretty flat and inconclusive, with estimates that have wobbled about a little but with no clear signal. This all changed with their latest result, in which the previous estimate of 27,100 cases (uncertainty range 19,300 - 36,700) in the week of 19 - 25 Aug increasing to 39,700 (29,300 - 52,700) in the week 30 Aug - 5 Sept. That is a rise of 46% in 11 days or about 3.5% per day. R is roughly the 5-day growth rate (for this disease), so that corresponds to an R value of 1.2, but note that their analysis doesn't extend over the past week when the cases have increased more sharply. </p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgaYcZH7Ydoh1mKSdylPzIBX7OgxwFM-IhqF5sOHFs-q3HYB4CpCYkftUlPHa6b44vC-yaQnUVitDm2ouF6yI5OwKXt9OGGwhAH3tDRf6sXffcpX4rWTMAtDguoevLM33d1K1c/s1380/Screen+Shot+2020-09-12+at+17.31.19.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="762" data-original-width="1380" height="276" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgaYcZH7Ydoh1mKSdylPzIBX7OgxwFM-IhqF5sOHFs-q3HYB4CpCYkftUlPHa6b44vC-yaQnUVitDm2ouF6yI5OwKXt9OGGwhAH3tDRf6sXffcpX4rWTMAtDguoevLM33d1K1c/w500-h276/Screen+Shot+2020-09-12+at+17.31.19.png" width="500" /></a></div><br /><p style="text-align: justify;"><br /></p><p style="text-align: justify;">Actually, I don't really think the ONS modelling is particularly good - it's a rather arbitrary curve-fitting exercise - but when the data are clear enough it doesn't matter too much. Just looking at the raw data that they kindly make available, they had almost 1 positive test result per 1000 participants over the fortnight 23 Aug - 5 Sept (55 cases in 59k people) which was 65% up on the rate for the previous fortnight of 26 cases in 46k people. Again, that works out at R=1.2.</p><p style="text-align: justify;">A rather worse perspective was <a href="https://www.gov.uk/guidance/the-r-number-in-the-uk" target="_blank">provided by SAGE</a>, who continue to baffle me with their inability to apply a bit of common sense and update their methods when they repeatedly give results so strikingly at odds with reality. They have finally noted the growth in the epidemic and managed to come up with an estimate marginally greater than 1, but only to the level of R=1.1 with a range of 1-1.2. And even this is a rounding-up of their estimate of daily growth rate of 1 ± 2% per day (which equates more closely to R=1.05 with range of 0.95-1.15). Yes, they really did say that the epidemic might be shrinking by 1% per day, even as cases are soaring and hospital admissions are rising. I do understand how they've managed to generate this answer - some of the estimates that feed into their calculation only use death data, and this is still very flat - but it's such obvious nonsense that they really ought to have pulled their heads out of their arses by now. I sometimes think my work is a bit artificial and removed from practical issues but their unwillingness to bend to reality gives ivory tower academics a bad name.</p><p style="text-align: justify;">At the other extreme, a <a href="https://www.imperial.ac.uk/media/imperial-college/institute-of-global-health-innovation/public/Resurgence-of-SARS-CoV-2-in-England--detection-by-community-antigen-surveillance.pdf" target="_blank">paper claiming R=1.7</a> was puffed in <a href="https://www.mirror.co.uk/news/politics/breaking-coronavirus-cases-now-doubling-22667035" target="_blank">the press</a> yesterday. It's a large survey from Imperial College, that bastion of incompetent modelling from the start of the epidemic. The 1.7 number comes from the bottom right hand panel in the below plot where they have fitted an exponential through this short subset of the full time series of data. There is of course a lot of uncertainty there. More importantly, it doesn't line up at all with the exponential fitted through the immediately preceding data set, starting at a lower level than the previous curve finishes. While R might not have been constant over this entire time frame, the epidemic has certainly progressed in a continuous manner, which would imply the gap is filled by something like the purple line I've added by hand.</p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiPXffofPUJpTRQ5ePA8lwd_63Y_KEPppvemiqSXjSs5tFozwHE9fSzbl6fUhDVjcpvG-nAMZmjPVVEeeYtzscwRKLg7OyE1JD8461DgfTIrbDrRD_MMR7Ore5GF9PUjyfwzDY/s1786/Screen+Shot+2020-09-12+at+17.04.59.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1362" data-original-width="1786" height="381" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiPXffofPUJpTRQ5ePA8lwd_63Y_KEPppvemiqSXjSs5tFozwHE9fSzbl6fUhDVjcpvG-nAMZmjPVVEeeYtzscwRKLg7OyE1JD8461DgfTIrbDrRD_MMR7Ore5GF9PUjyfwzDY/w500-h381/Screen+Shot+2020-09-12+at+17.04.59.png" width="500" /></a></div><div style="text-align: justify;"><br /></div><p style="text-align: justify;"><br /></p><p style="text-align: justify;">It's obviously stupid to pretend that R was higher than 1 in both of the recent intervals where they made observations, and just happened to briefly drop below 1 exactly in the week where they didn't observe. The sad thing about the way they presented this work to the media is that they've actually done a rather more sensible analysis where they fit the 3rd and 4th intervals simultaneously, which is shown as the green results in the 3rd and 4th panels on the top row of the plots (the green in the 3rd panel is largely overlain by blue which is the fit to 2nd and 3rd intervals, but you can see if you click for a larger view). Which gives.....R=1.3. Who'd have thought it?</p><p style="text-align: justify;">Of course R=1.7 is much more headline-grabbing. And it is possible that R has increased towards the end of their experimental period. Rather than fitting simple exponentials (ie fixed R values) to intervals of data, perhaps a more intelligent thing to do would have been to fit an epidemiological model where R is allowed to vary through time. Like I have been doing, for example. I'm available to help and my consultancy rates are very reasonable.</p><p style="text-align: justify;">In conclusion, R=1.3(ish) but this is a significant rise on the value it took previously and it might well be heading higher.</p>James Annanhttp://www.blogger.com/profile/04318741813895533700noreply@blogger.com8tag:blogger.com,1999:blog-9959776.post-11720525617231008822020-08-05T20:30:00.003+01:002020-08-05T20:58:51.947+01:00Could R still be less than 1?<div style="text-align: justify;">It's been suggested that <a href="https://www.bbc.co.uk/news/health-53656852" target="_blank">things might all be fine</a>, maybe the increase in case numbers is just due to more/better testing. There certainly could be a grain of truth in the idea, as the number of tests undertaken has risen a little and the proportion of tests that have been positive has actually kept fairly steady over recent weeks at around 1%. On the other hand, you might reasonably expect the proportion of positives to drop with rising test numbers even if the number of ill people was constant, let alone falling as SAGE claim - consider at the extreme, 65 million tests couldn't find 650,000 positives if only a few tens of thousands are actually ill at any one time. Also, the <a href="https://www.ons.gov.uk/peoplepopulationandcommunity/healthandsocialcare/conditionsanddiseases/bulletins/coronaviruscovid19infectionsurveypilot/31july2020">ONS pilot survey</a> is solid independent evidence for a slight increase in cases, albeit not entirely conclusive. But let's ignore that inconvenient result (as the BBC journalist did), and consider the plausibility of R not having increased in recent weeks. </div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">This is fairly easy to test with my data assimilation system. I can just stop R from varying at some point in time (by setting the prior variance on the daily step to a negligible size). For the first experiment, I replaced the large jump I had allowed on 4th July, with fixing the value of R from that point on. Note however that the estimation is still using data subsequent to that date, ie it is finding the (probabilistic) best fit for the full time series, under the constraint that R cannot change past 4 July. I've also got a time-varying case ascertainment factor which I'll call C, which can continue to vary throughout the full interval.</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">Here are the results, which are not quite what I expected. Sure, R doesn't vary past the 4th of July, but in order to fit the data, it shoots up to 1 in the few days preceding that date (red plume on 2nd plot). The fit to the death data in the bottom plot looks pretty decent (the scatter of the data is very large, due to artefacts in the counting methodology) and also the case numbers in the top plot are reasonable. See what has happened to the C factor though (red plume on top graph). After being fairly stable through May and most of June, it takes a brief nose-dive to compensate for R rising at the end of June, and then has to bounce back up in July to explain the rise in case numbers.</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;"><br /></div><div><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjwheruBiPHbuSQ2nZOw9Rz6jVFYnrKlSnURHjEPGzd08ocKs_EXqZAU-CCc21XOrusuj2PAwy6LZhHRiF5t3jc0zmIPZGaIGCYLuN1Ifo9tBzgBgHg9aDPw9wu9RVWzuovBtY/s1352/uk_04_aug_c_july.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="835" data-original-width="1352" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjwheruBiPHbuSQ2nZOw9Rz6jVFYnrKlSnURHjEPGzd08ocKs_EXqZAU-CCc21XOrusuj2PAwy6LZhHRiF5t3jc0zmIPZGaIGCYLuN1Ifo9tBzgBgHg9aDPw9wu9RVWzuovBtY/s640/uk_04_aug_c_july.png" width="640" /></a></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg-_dgxfYOYHD-ChYoa4CEitJKtimk90WedvRDv-5nEq-Bimjwc0FRIhdhd7jP1xt46_-vCKmHR_WI8L_S7bipT63fTzKUOWHmxTIdoHRjMX58onZN7M1hwVhxH7RBSWmm7Uvw/s1352/uk_04_aug_d_july.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="835" data-original-width="1352" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg-_dgxfYOYHD-ChYoa4CEitJKtimk90WedvRDv-5nEq-Bimjwc0FRIhdhd7jP1xt46_-vCKmHR_WI8L_S7bipT63fTzKUOWHmxTIdoHRjMX58onZN7M1hwVhxH7RBSWmm7Uvw/s640/uk_04_aug_d_july.png" width="640" /></a></div><div><br /></div><div style="text-align: justify;"><div>While this isn't impossible, it looks a bit contrived, and also note that even so, we still have R=1, firmly outside the SAGE range of 0.8-0.9. Which isn't exactly great news with school opening widely expected to raise this value by 0.2-0.5 (<a href="https://www.theguardian.com/world/2020/aug/05/neil-ferguson-predicts-r-number-rise-if-secondary-schools-fully-reopen">link1</a>, <a href="https://www.thelancet.com/journals/lanchi/article/PIIS2352-4642(20)30250-9/fulltext">link2</a>).</div><div><br style="text-align: left;" /></div></div><div style="text-align: justify;">So, how about fixing R to a more optimistic level, somewhere below 1? My code isn't actually set up very well for that specific experiment, so instead of holding R down directly, I just put the date back at which R stops varying. In the simulations below it can't change past the 1st June. It still climbs up just prior to that date, but only to 0.9 this time, right at the edge of the range of SAGE values. The fit to the death data is similar, but tis time the swoop down for C on the upper plot is a bit more pronounced (because R is higher through June) and then it has to really ramp up suddenly in July to match the rise in case numbers. You can see that it starts to underestimate the case numbers towards the present day too, C would have to keep on ramping up even more to match that properly.</div><div><br /></div><div style="text-align: justify;"><br /></div><div><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh9xfHF6Jp3koxb27lcZR92Yewy2-DHWMfe-CoQxKHRYO2bHxa9Co7hGtKadZrMihHqn3DbHySqCEQ5j-mEp-CsfNd2f-HDU_wW0QOaydwQgl-dGpHULZugi2YMKhd22CbRq3g/s1352/uk_04_aug_c_june.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="835" data-original-width="1352" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh9xfHF6Jp3koxb27lcZR92Yewy2-DHWMfe-CoQxKHRYO2bHxa9Co7hGtKadZrMihHqn3DbHySqCEQ5j-mEp-CsfNd2f-HDU_wW0QOaydwQgl-dGpHULZugi2YMKhd22CbRq3g/s640/uk_04_aug_c_june.png" width="640" /></a></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiWIwizJ7_uLClIix__Auo_-6wIkDE7t4SdGutCBfPob9-sKvmWA0v4ktQfgjtWBqZhyphenhyphenduhdNMgM1oSToBZ3dHukN7U5VEgTsR64xILgvs4LhtDDMHIcIL-hGySszuMD6iKQRM/s1352/uk_04_aug_d_june.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="835" data-original-width="1352" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiWIwizJ7_uLClIix__Auo_-6wIkDE7t4SdGutCBfPob9-sKvmWA0v4ktQfgjtWBqZhyphenhyphenduhdNMgM1oSToBZ3dHukN7U5VEgTsR64xILgvs4LhtDDMHIcIL-hGySszuMD6iKQRM/s640/uk_04_aug_d_june.png" width="640" /></a></div><div><div style="text-align: justify;">So R being in the SAGE range isn't completely impossible, but requires some rather contrived behaviour from the rest of the model which doesn't look reasonable to me. I don't believe it and think that unfortunately there is a much simpler explanation for (some of) the rise in case numbers.</div></div>James Annanhttp://www.blogger.com/profile/04318741813895533700noreply@blogger.com3tag:blogger.com,1999:blog-9959776.post-11640783775401662122020-08-05T15:19:00.004+01:002020-08-05T16:16:05.695+01:00More what-ifs<div style="text-align: justify;">It was pointed out to me that <a href="https://julesandjames.blogspot.com/2020/08/what-if.html" target="_blank">my previous scenarios</a> were roughly comparable to those produced by some experts, specifically this <a href="https://www.bbc.co.uk/news/health-53515077" target="_blank">BBC article</a> referring to <a href="https://acmedsci.ac.uk/file-download/51353957" target="_blank">this report</a>. And then <a href="https://www.bbc.co.uk/news/health-53638083" target="_blank">yesterday</a> another <a href="https://www.thelancet.com/journals/lanchi/article/PIIS2352-4642(20)30250-9/fulltext" target="_blank">analysis</a> which focussed on schools opening.</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">The experts, using more sophisticated models, generated these scenarios (the BBC image is simplified and the full report has uncertainties attached):</div><div><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh_mfqcOjlwVvb7uMg66AYGVveN_RLONVM8rpuT5IVdzHeADtSU21vt3Ol7tyTw44SywA4gX5K2OLgqlpHh99L2mw-59OqcXewXh6RwO1fojyqv5-LEkxJD79nW027-swDqI-g/s2048/bbc.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1084" data-original-width="2048" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh_mfqcOjlwVvb7uMg66AYGVveN_RLONVM8rpuT5IVdzHeADtSU21vt3Ol7tyTw44SywA4gX5K2OLgqlpHh99L2mw-59OqcXewXh6RwO1fojyqv5-LEkxJD79nW027-swDqI-g/s640/bbc.png" width="640" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: justify;">and for the schools opening report:</div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiRHuNn7Aw9JGipRziBTaqXJlKCT1zqZ9jPnAfe0yGCXD5liGNtXOqvyzApfg2fRUj1Th9UpVbeTE38Voi-2bcnw3oU7iCjo4ESy8ouahkuZilYqnwgGxxU18EAzuSPf5AGBkM/s2072/Screen+Shot+2020-08-05+at+15.04.17.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="728" data-original-width="2072" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiRHuNn7Aw9JGipRziBTaqXJlKCT1zqZ9jPnAfe0yGCXD5liGNtXOqvyzApfg2fRUj1Th9UpVbeTE38Voi-2bcnw3oU7iCjo4ESy8ouahkuZilYqnwgGxxU18EAzuSPf5AGBkM/s640/Screen+Shot+2020-08-05+at+15.04.17.png" width="640" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: justify;">The tick marks are not labelled on my screenshot but they are at 3 month intervals with the peaks being Dec on the left hand and March on the right hand panel.</div><div class="separator" style="clear: both; text-align: justify;"><br /></div><div class="separator" style="clear: both; text-align: justify;">While these are broadly compatible with <a href="https://julesandjames.blogspot.com/2020/08/what-if.html" target="_blank">my analyses</a>, the second peak for both of them is significantly later than my modelling generates. I think one important reason for this is that my model has R a little greater than 1 already at the start of July, whereas they are assuming ongoing suppression right through August until schools reopen. So they are starting from a lower baseline of infection. The reports themselves are mutually inconsistent too, with the first report having a 2nd peak (in the worst case) that is barely any higher than the first peak, and the second report having a markedly worse 2nd peak, despite having a substantially lower R number over the future period that only briefly exceeds 1.5. It's a bit strange that they differ so significantly, now I think about it...I'm probably missing something obvious in the modelling.</div><div><br /></div><div>Of course in reality policy will react to observations, so all scenarios are liable to being falsified by events one way or another.</div>James Annanhttp://www.blogger.com/profile/04318741813895533700noreply@blogger.com0