In this seminar, a general stochastic framework for modelling the course of a complex epidemic. Although this class of models can incorporate fine modelling details (many compartments, non-exponential waiting times, complex correlations, etc), I will show that their large scale behavior is well described by means of a simple partial differential equation of the Kermack-McKendrick type. I will discuss how this approach relates to more classical ones, based on sets of ordinary differential equations of the SIR type. Finally, I will provide some theoretical predictions of the models on the distribution of transmission trees in the population, that could be applied to contact-tracing data.

Félix Foutel-Rodier originally trained as an evolutionary biologist at the École Normale Supérieure (Paris) but have completed my Ph.D. in probability theory at Sorbonne Université and at the Collège de France in Paris. My research work first focused on stochastic models motivated by questions arising from population genetics. Since the onset of the COVID-19 epidemic, I have been interested in epidemic modeling and I have recently started a postdoc at the Université du Québec à Montréal (Montreal) on this topic, which is partly funded by the MfPH program.