Our approach

The logistic function

We found that the logistic function can be used to modelise various kind of epidemiologic data such as the number of confirmed cases, the number of hospitalisation or the number of deaths. After performing regressions, we found that the calculated functions surprisingly fit many reported data, with NRMSE (Normalised Root Mean Square Error) usually below 0.1%. This excellent fit can be observed at different geographic scales (we studied country-level data as well as smaller geographical subdivisions such as provinces or cities).

To get an understanding about the logistic function and its relevance to epidemics, you can watch this excellent video from Grant Sanderson (3blue1brown) :

Regressions over time

If the model is relevant, we should observe the following as we gather more data :

- Decreasing NRMSE
- The 3 degrees of freedom of the logistic curve should also converge

What can we learn from those regressions?

Regressions will provide the values of the 3 parameters / degrees of freedom of the logistic curve:

- Its maximum (L),
- The abscissa of its midpoint (x0), and
- Its growth rate (k)

The abscissa of the curve's midpoint is probably the most interesting information of all: it indicates when the peak of the epidemics will occur / occurred.

We can observe that this parameter is correlated to several factors such as the public policies, apparent behaviour of the population, etc.