Update: Apr. 13th, 2020

Covid-19: Peak... what peak? The worst possible time to relax social distancing

by nicolas busca

The spread of an infectious disease has a complicated dynamics. In the simplest model, which I discussed in my previous post, there are three variables to track down (number of people who haven't been infected yet, number of people who are currently infected and number of people who have gone through the infection) and the equations that describe their time evolution are non-linear.

There's quite a lot of confusion as to what the "peak" means and what it means to have "passed the peak". There are two numbers that are updated almost hourly in red characters on TV, the number of new confirmed cases and the number of new deaths, and those numbers are going to have their respective peaks. The model I've implemented predicts that we are very close to seeing a peak in the daily number of confirmed and deaths, or even that we have already seen it. It is tempting to conclude that the worst is over and there's no reason to be so uptight about social distancing anymore. Unfortunately, that's a bit of a dangerous conclusion.

But why is it wrong to think that the worst is over? Let's look at how many infected people the model predicts. This is the peak that we should really be following, since more infected people means higher contagion probability. Social distancing measures should only be relaxed after the number of infections has significantly gone down. This number doesn't get reported since it's very hard to measure, but we can use the model there.

The figure below compares the expected curves for the new daily confirmed cases, what we are all tracking, and the total infected, what we should really care about (I've renormalized the curves a bit to make them both visible on the same scale). Note how the infected curve is displaced compared to the curve of new cases (the number we get bombarded with on TV every day). The total number of infections will start going down once the rate of new infections is lower than the rate of recovered (or deaths). For that to happen, the number of confirmed cases and deaths has to go steadily down for a few days. But that's not enough. In Romania, according to the model, the peak of infections will come when the number of new daily confirmed cases has gone down to about 280 and the number of daily deaths down to about 20 and about a week after the peak in the number of daily reported cases.

The good news is that is not that far in the future. The bad news is that if we wait for a number of infections to go significantly down before we see sunshine other than through the window, that means at least mid-may. And we should definitely wait for it.