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Thematic Line: Biomathematics

9 January 2023, 4:00 p.m. to 4:45 p.m.

Seminar of Biomathematics

Title: Modeling and analysis of complex epidemic events using hybrid dynamical systems

Speaker: Guillaume Cantin (Département Informatique, UMR_6004 Laboratoire des Sciences du Numérique de Nantes, Nantes Université)


In this talk, I will present recent works realized in collaboration with Cristiana J. Silva on the modeling and analysis of complex epidemic events.

In the first part, I will show how to model the spatial spreading of an epidemic in a heterogeneous geographical environment using complex networks of dynamical systems. 

The influence of the topology of the underlying network on the dynamics of the epidemic will be illustrated with a theoretical approach for small networks, and with a computational approach for large networks.

In the second part, I will present a novel approach for studying the impacts of human behaviors on the spreading of an epidemic, using hybrid dynamical systems coupling a macroscopic approach relying on differential equations with a microscopic individual-based approach.

Theoretical results on the well-posedness of such hybrid models and on the existence of particular solutions exhibiting irregular oscillations will be exposed.