Here is their current plot for the UK:
I've checked their results. And it confirms what I was worried about.
I got the data from https://datahub.io/core/covid-19#resource-time-series-19-covid-combined
I tried fitting a classic SIR model, solved via simple Euler. However I didn't trust my numerics. With a small removal rate of infectives which is what I suspected they had found for most countries (because of the symmetry in their plots) there is a simple formula for infectives. So I fitted that and got the following:
However, the SIR model has two parameters in the odes, and two initial conditions. As I said, I had one parameter being zero. One initial condition, for number of infected, was easy. I started at I=85. That leaves just the infection rate and initial number of susceptibles, S_0, for fitting.
The best fit had S_0=140,000. That's what I was worried about.
What they have done, it seems, is fit a perfectly decent model to an uncontrolled infection in a rather sparsely populated island. That is not the same as what we have, an infection in an island with a large population with lockdown.
At the moment it looks like something I said weeks ago: All models give the same shape curve. Which is the right one? Why not just fit any S-shaped curve (to totals), and not worry about justifying the model?
If their results turn out to be correct then I think it's more luck than anything. For zero removal rate the solution of the odes is the logistic function
. Which is probably the function you'd choose for fitting in the absence of a model anyway!!!
Cuch, if you're feeling strong you could repeat this with non-zero removal rate. As I also said, the data suggests for many countries that it is non zero because of the slower decay after the peak, than the growth before. (I.e. asymmetry.)