Modelling the Propagation of Epidemics with Diffusion

Abstract

Various diffusion mechanisms are key to the propagation of epidemics.  As a matter of fact, diffusion arises under several guises in epidemiology. After reviewing some classical results, the speaker will present recent works that deal with diffusion and were motivated by the Covid-19 pandemic. He will first discuss models of spatial spreading of epidemics. Then, he will present a new model for the dynamics of epidemics that includes the effects of heterogeneity of individual behaviors and social diffusion. He will show that this model yields rich dynamical structures that exhibit outstanding features of epidemics such as the formation of plateaus, “shoulders” and rebounds, as were observed in the dynamics of the Covid-19 epidemics. He will discuss results we have obtained on this system, and some challenges it raises. He reports here on joint work with B. DESJARDINS, J. Weitz, and J-M. OURY.

About the Speaker

Prof. Henri Berestycki received his PhD from Université Pierre et Marie Curie in 1975, and was a CNRS researcher at the University of Paris VI before joining the University of Paris XIII as a Professor in 1983. He then returned to Université Pierre et Marie Curie as a Professor of Mathematics in 1988. In 2001, he moved to École des Hautes Études en Sciences Sociales (EHESS, which became a constituent college of the federal PSL Research University later), where he is currently a Professor. He was appointed the Dean of Research in PSL Research University in 2015-2017.

Prof. Berestycki’s current research interests include the mathematical modelling of financial markets, mathematical models in biology and especially in ecology, and modelling in social sciences.

Prof. Berestycki received numerous awards including the Sophie Germain Prize of the French Academy of Sciences (2004); the Gay-Lussac-Humboldt-Prize of the Humboldt Foundation (2004); the French Legion of Honor (2010). He was selected as a Fellow of the American Mathematical Society and an International Honorary Member of the American Academy of Arts and Sciences in 2013.

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