Henri Berestycki

Centre d’analyse et mathématique sociales CNRS and École des hautes études en sciences sociales (EHESS), Paris

Reaction-diffusion systems in epidemiology

The classical SIR type equations of epidemiology that take into consideration spatial spreading lead to reaction-diffusion systems. Such systems also arise in the study of collective behaviors such as riots. In this lecture, I will first recall the classical setting and then discuss a general framework for this type of systems that we call “Activity / Susceptibility” systems. In the second part of my talk, I will present a new model that describes the influence of roads on the spread of epidemics. If time permits I will also show applications of these ideas to data of the current Covid-19 epidemics. I report here on joint work with Samuel Nordmann and Luca Rossi for the first part, with Jean-Michel Roquejoffre and Luca Rossi for the model with roads and with Lionel Roques et al. for the study of data.