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:

Very similar.

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.)