Saturday, April 04, 2020

Are we achieving suppression in the UK?

Some people are talking about a peak in deaths over the next week or two. And suppressing the disease such that we might be able to lift the lockdown eventually (end of May has been mentioned). But when will we tell how well the controls are working? I've already shown that it takes a while to really show up convincingly in the daily death data (and I haven't even taken account of additional delays in reporting deaths once they've happened). Clearly the reported case numbers for illness are wholly inaccurate and reflect testing policy more than anything else.

Here are a few hypotheticals, again based on the SEIR model fit to daily death data. This time, I have tried a few scenarios in which the effectiveness of the lockdown is measured as a scaling on the R0 parameter. In order from top to bottom, in the plot below R0 stays the same, then is reduced by 50%, 75% and 95% of its value, at the date of the lockdown. The two end cases are IMO wholly implausible and I've put them in just to show the bounds of what the model could do.

First the daily death figures, with recent observations shown. The data don't distinguish much between the scenarios, though you could say it's slightly optimistic that the most recent couple of days are towards the lower end of the spread, but still compatible with even the blue plume at this stage. The plumes do separate out a bit and in another week we will have a much clearer picture of which is closest to the truth. The original R0 in this fit is 3.3 so the green plume with Rt = 1.6 is still trending up towards a widespread epidemic whereas the red one with Rt = 0.8 is achieving control at a much lower level, albeit taking a bit of time to do so. 

The yellow plume shows that people keep on dying at much the same rate for a while even if the disease is quickly reduced with Rt = 0.16. This is a consequence of the long time that some people take to die - at least according to the fitted distribution of time to death that I've taken from the Ferguson et al work. I think it may be worthwhile to revisit this time to death as it was based (as so much of the modelling has been) on a very small set of Chinese data from early on in their outbreak. Rather amazingly, the entire shape and size of the time-to-death distribution beyond 20 days is based on the extrapolation of a parametric fit into a region which contains not a single data point. I'm not saying it's wrong and they probably did as good a job as was possible with the limited data available at that time, but it could surely be improved (revalidated) now.

I've said I don't believe the data on reported cases, but the level of illness is still something that the healthcare system experiences and it's possible that this will provide an earlier indicator. If fewer people are getting ill then there will be fewer 999 calls and lowered demand on beds etc. The symptomatic cases respond much more rapidly and clearly to controls, as shown below. 

So in the red case of even marginal control, where Rt is just over 0.8 on average, the number of new cases falling ill each day should be dropping off quite quickly (consistently by about 5% per day) and by now be well down from their peak. This may not be immediately felt if the beds are still full of course, but it could be observable soon even if time from symptomatic to seriously ill is another week (some people die faster than this). It will certainly be clear soon enough if the cases are really dropping.


Everett F Sargent said...


Here are two of the doubling time plots, have a look ...

Problem countries: US, UK and maybe FR
Recovery countries: IT, ES, and maybe DE and maybe Benelux.

James Annan said...

Neeed More Label!

Everett F Sargent said...

As in, need more cowbell? :)

The spaghetti plots are rather busy, that I will admit. But then again, I've gotten use to it since I've been looking at them for at least 10 days. I tried my best on the colors, where nine appears to be the upper limit.

Everett F Sargent said...

Oh and I'm nearsighted 20/400 (or worse), so that I have two built-in magnifying glasses, I can get within ~10 cm of anything and it will be in focus, say like 10X.

Everett F Sargent said...

Oh and four years of technical drafting (from 1967-72, I was always 1st in drawing the third view given the other two), a two year technical degree (AAS in CE), land surveying, BS and MS in CE, so that's almost like 53 tears of looking at technical drawings.

Note to self: I don't, in any way, consider the above traits an advantage, in fact, I consider them a disadvantage.

Everett F Sargent said...

Oops, so I can't even count, "1967-72" should be "1968-72" and "53 tears" should be "52 years" sorry about that.