The Imperial College code

The Imperial College code, the results from which are thought to have changed the UK government’s coronavirus policy, has been available for a while now on github. Since being made available, it’s received criticism from some quarters, as discussed by Stoat in this post. The main criticism seems to be that if you run the model twice, you don’t get exactly repeatable results.

As Stoat, points out, this could simply be due to parallelisation; when you repeat a simulation the processors won’t necessarily return their results in the same order as before. However, it could also be due to other factors, like not quite using the same random number seed. These simulations are intended to be stochastic. The code uses random numbers to represent the probability of an outcome given some event (for example, a susceptible person contracting the virus if encountering an infected person). Different runs won’t produce precisely the same results, but the general picture should be roughly the same (just like the difference between weather and climate in GCMs).

For a while now I’ve been playing around with the Imperial College code. I should be clear that I’m not an epidemiologist and I haven’t delved into the details of the code. All I’ve been doing is seeing if I can largely reproduce the results they presented in the first paper. The paper gives much more detail about the code than I intend to reproduce here. However, it is an individual-based model in which individuals reside in areas defined by high-resolution population density data. Census data were used to define the age and household distribution size, and contacts with other individuals in the population are made within the household, at school, in the workplace and in the wider community.

I’ve run a whole suite of simulations, the results of which are shown on the right. It shows the critical care beds, per 100000 of the population, occupied under different scenarios. If you’ve downloaded the paper, you should see that this largely reproduces their Figure 2, although I did have to adjust some of the parameters to get a reasonable match. The different scenarios are Do nothing, Case Isolation (CI), Case Isolation plus Household Quarantine (CI + HQ), Case Isolation, Household Quarantine plus Social Distancing of the over 70s (CI + HQ + SD70), and Place Closures (PC). To give a sense of the severity, the UK has just under 10 ICU beds per 100000 of population.

I’ve also included (dashed line) the scenario where you impose Case Isolation, Place Closure (Schools and Universities) and general Social Distancing for 150 days (which they show in their Figure 3). As you can see, this really suppresses the infection initially, but there is a large second peak when the interventions are lifted. This is what, of course, is concerning people at the moment; will the lifting of the lockdown in some parts of the UK lead to a second wave?

So, I seem to be able to largely reproduced what they presented in the paper. This doesn’t really say anything about the whether or not the results are reasonable respresentations of what might have been expected, but it’s a reasonable basic test. I will add, though, that there are a large number of parameters and I can’t quite work out how to implement the somewhat more dynamic intervention strategies.

Something else I wanted to add is that I’ve also played around with some other codes, including a simple SIR code, a SEIR code, and one that included an age distribution and a contact matrix. Whatever you might think of the Imperial College code, all of the models seem to suggest that without some kind substantive intervention, we would have overrun the health service.