Clive Harrison is an old friend and a water sector professional with a fine gasp of modelling that get to the essence of complex problems even when the data is poor. While stuck in Poland because of travel restrictions due to COVID-19, he turned to modeling to understand the pandemic. The result was an easy-to-use Excel model where anyone can enter their own assumptions about key variables such as social distancing and doubling time of the virus, and see how changes in those variables change the rate of infection and death in various countries. Clive has agreed to share this model which might be helpful for people trying to understand the basic dynamics of the epidemic. Clive has also shared his thoughts about modeling in situations like this. Please feel free to download the model at the end of this post, and do let us know if you make improvements to the model.David Ehrhardt, Chief Executive, Castalia
Clive Harrison is the guest author of the blog post below.
In the absence of of any hard data I turned to modelling to try to figure out what’s really happening with the pandemic. It’s very simple, deterministic stuff but it seems to work quite well. It’s fun but a bit scary to play with the assumptions (highlighted in yellow in the model). I pulled in the latest stats on reported deaths in each country and calibrated my models for Canada (almost exactly the same population as Poland), Sweden (it looks as they are within a few days peaking out, without any formal social distancing), the USA (don’t look, it’s awful) and the UK (ditto). India would be interesting to look at but I don’t have the stomach for that yet.
I noticed the little piece in the Economist a week or so ago, on a pre-peer-review paper by Silverman and Washburne on “using ILI surveillance to estimate state-specific case detection rates” to estimate the unreported COVID-19 cases and then project their growth. ILI stands for Influenza-Like Illness, and the Obama administration set up a system where panels of GPs in each State report the weekly numbers of patients consulting them with flu-like symptoms but who test negative for flu. Apparently there is a very unusual spike in these reports that coincides and correlates with the early Covid-19 case reports but is many times larger (i’m attaching it in case you didn’t see it). The implication is that the number of infectious cases is much larger than current estimates and thus that the death rate is commensurately lower and the spread much quicker.
There’s also a recent study based on surveys in Heinsburg, Germany, that reportedly estimates the death rate there at just under 0.5%, so I took that as my upper bound and then modeled for death rates of 0.1% and 0.5% to see what difference they make. If confirmed then it means that the epidemic will peak and fade more quickly than present estimates suggest and that there would be mercifully fewer deaths. Sweden will show the way in the next few days probably, as their case and death rates are spiking and could peak and start to fall in the next week or two.
The model assumptions are very simple: the basic infection rate is defined as the time for cases to double, nobody gets infected a second time, the proportion of susceptible individuals shrinks as the proportion of people who are or were infected increases, and social distancing slows the rate of growth by increasing the doubling time. I calibrated the models by adjusting the date of the first infection, the doubling time, the multiplier for the impact of social distancing and the number of days after the start of the epidemic before social distancing was introduced (but I didn’t check whether this matched the actual date). The third chart to the right of the table shows the actual reported deaths as blue dots and the model values as lines, orange with social distancing and blue without. The main formulae are in cells C14 and K14 and then just copied down.
If the epidemic is going to be over more quickly than the press would have us believe, then there will be many interesting consequences that I am only beginning to think about.
Photo by Fernando Zhiminaicela