Tuesday, March 10, 2020

BlueSkiesResearch.org.uk: Coronavirus

This is mostly an excuse to publish a blogpost using Rmarkdown. This is a system for combining R code in a "markdown" text document which can be readily compiled into html or pdf etc and also automatically published on WordPress which hosts the Blueskiesresearch blog. One slight problem I've not been able to solve is how to handle graphs: while I can automatically generate them as separate files (eg png format) I can't automatically upload them to WordPress and so have to manually edit the post and fix the figures after compiling and uploading the post. If any readers know how to automate this, I'd like to hear about it. Anyway, on with the show.

Before I start I should point out that I have no particular authority to speak on this topic. I'm writing about coronavirus COVID-19 from a position of no more knowledge than anyone else who has followed the media. I hope I'm being pessimistic but I do think it's likely to be a major problem. The 1%(ish) mortality rate is not the reason. A bit more than 1% of the population dies in any given year and if a substantial additional chunk of people, the vast majority of who are already suffering from health challenges, were to die a little quicker than expected then it would be sad for them and their families but the broader impact would be modest.

The real problem appears to me to be the combination of (a) roughly 10-20% needing hospital treatment ranging up to the level of intensive care and (b) the rapidity of the spread of the virus when unchecked by social distancing. To put it simply, if we all get ill at the same time there is not the capacity to treat a significant population in hospital. England has enough hospital beds for 0.04% of the population — the lowest in the developed world, for which we can all thank the Tories, but there's no point banging on about that as it's not going to change in the next 3 months. Less than a tenth of these are intensive care beds – enough for about 0.0035% of the population at any one time. Say 2000 beds. If people (optimistically) need only 5 days in hospital then we can treat 400 new people each day, meaning 4000 cases per day (at a 10% hospitalisation rate) is the limit of our capacity. More than that, and people with serious breathing difficulties simply won't be treated. Which will put the death rate up, perhaps substantially.

I've seen graphics representing the impact of social distancing and other ways of slowing the spread, but they seem mostly rather schematic. I thought it would be nice to have some actual calculations. So here are a few simple logistic simulations based on different doubling times and total penetration of the epidemic. All of them start out with a total of 300 cases on the 9th March. Recent data in the UK and also Italy, Germany has suggested a rather rapid doubling time of around 3 days but I am hoping that's a bit of a blip due to catching up on cases and/or that it could be easily stretched out a bit by people behaving a bit more cautiously. Taking a look at Japan, they are taking significant but not draconian action and their doubling time is more like a week. As well as different doubling times, the red, blue and orange curves also have a different total penetration of 80%, 60% and 40% respectively of the UK population. These are largely guesses on my part but slower spread does also generally mean more people manage to avoid it. There is also the effect of summer with warmer/drier weather, which we may hope to help reduce spread. I haven't explicitly accounted for this.
The green line is the most fictional of the lot, it is my presentation of what capacity we might currently have and what the effect could be of ramping this up. As described above, I've assumed as a starting point that we can currently cope with 4000 new cases per day — probably optimistic in itself, but hopelessly inadequate in the face of an uncontrolled epidemic. The area that lies under each epidemic curve but above the green line represents the number of cases that will exceed the capacity to treat them (well actually it's 10 times that number, under my assumption of a 10% hospitalisation rate). My additional assumption is that we can ramp this up with a doubling time of 14 days. I should emphasise this is just make-believe for the sake of plotting pretty graphs and is in no way an informed estimate. Ramping up capacity has almost no effect for the red curve, but it would mean a far higher proportion of cases being properly treated for the blue curve and would keep us ahead of the orange curve — even though the epidemic growth rate in that case is initially more rapid than the capacity growth rate. If capacity is not increased, however, even the orange case would be very challenging for our health care system. While I don't want these simple calculations to be taken too seriously, they do suggest that working out how to treat people adequately and efficiently with limited resources might be an important part of the solution. But we certainly have to do what we can to stretch out the doubling time beyond a week at least.

Let's hope I'm wrong and that these graphs are shown to be hopelessly pessimistic. Here are a few ways that things could turn out better:
* There may be a much higher proportion of mild cases (often undetected and non-infectious) meaning less hospital treatment required as a proportion of total cases.
* Warming weather may slow the spread substantially from May onwards.
* We may actually be able to slow the doubling time down substantially with a bit more attention to hygiene and social distancing without completely killing the economy.

For some perspective, the "Spanish" flu pandemic of 1918 infected about 1/3rd of the global population and killed 2–3% of these (Wikipedia numbers). The numbers I've presented are worse in some ways but not wholly incomparable. We do have much stronger connectivity these days and COVID-19 seems to be quite challenging in various ways.

If people have ideas for more credible calculations I can easily test them out. But I don't want anyone to suffer under the misapprehension that this is in any way authoritative or believable. It's just lines on a screen.


Arthur said...

Japan's curve seems different to that of Europe. See

David B. Benson said...

Under 60 you will be fine in a few days. Only older folk require care.

David B. Benson said...

A surgeon publicly commented that even here in Washington state most intensive care beds are unoccupied.

James Annan said...

Li Wenliang was only 34. The first locally transmitted case in Italy was a fit 38 year old who only just got out of intensive care after 2 weeks in hospital. Most people aren't seriously ill, the problem is that a significant proportion are.

Washington state has only had a couple of hundred cases. Of course it's got bed space currently. Come back and update us in a week will you?