Including diffusion in the classical framework of SIR equations in epidemiology leads to reaction-diffusion systems. In epidemiology, diffusion arises under several guises. After reviewing some classical results, I will present recent works that deal with diffusion and were motivated by the ongoing Covid-19 pandemic. If time permits, I will talk about: 1) a model of spatial spreading of Covid 19 in France with diffusion on graphs; 2) the effects of fast diffusion on lines such as roads; and 3) the effects of individual behaviors and social diffusion on the dynamics of epidemics.

Bio: Henri Berestycki is a French mathematician who studied at Ecole normale supérieure in Paris and obtained his PhD from Sorbonne Université. He has made fundamental contributions to nonlinear partial differential equations and opened new areas in modeling. His research concerns the Qualitative Theory of Nonlinear Parabolic and Elliptic PDE’s, Reaction– Diffusion Equations, and Propagation Phenomena. His work is in dialogue with Physics, Biology, Ecology, Epidemiology, and Social Sciences. Henri Berestycki holds the chair of “Mathematical Analysis and Modeling” since 2001 at Ecole des hautes études en sciences sociales (EHESS) in Paris. He is Senior Visiting Fellow of the Institute of Advanced Studies of Hong Kong University of Sciences and Technology since 2018. Among numerous awards and distinctions, he received the Gay-Lussac - Humboldt Prize (2004) in Germany, the Sophie Germain Prize of the French Académie of Sciences (2004) and is a foreign Honorary Member of the American Academy of Arts and Sciences (since 2013). He was the recipient of an ERC Advanced Grant (2013-2018) on Reaction Diffusion Equations and Propagation Phenomena.