CMX Lunch Seminar

We show that the Gompertz Function provides a generically excellent fit to viral and bacterial epidemics and endemic data. There is a ‘good' Gompertz Function fit for each time t, starting very early in any outbreak. Successive fits provide excellent forecasts for extended periods.

Examples include Influenza in 2017-18 and Covid-19 in the Spring of 2020 and the ‘second waves'.

The Gompertz Function's features have consequences for herd immunity and for the transition from epidemic to endemic diseaseâ€"which we argue is what we are now seeing in the so-called second waves.

We conjecture that the accuracy of the Gompertz Function fits is not a coincidence but reflects the human immune response to viral and bacterial infections that has evolved over millions of years. Based on the Gumbel distribution, which is one of the exceptional distributions for the geometry induced by the action of the ‘location-scale' group, it has a natural Hamiltonian structure an the energy is a key observable of the epidemic dynamics.

Finally, we illustrate the use of Extreme Value Theory to predict potential surges in the early phase of outbreaks where the Gompertz Function's predictive power is lowest.

The talk is based on joint work with Ana Cascon.