Institut de Mathématiques de Marseille, UMR 7373




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Studying the spread of evolving diseases : traveling waves and pulsating fronts.

Mardi 20 juin 11:00-12:00 - Quentin GRIETTE - Institut Montpelliérain Alexander Grothendieck

Studying the spread of evolving diseases : traveling waves and pulsating fronts.

Résumé : I will talk about a system of two coupled reaction-diffusion equations modeling the spread of evolving diseases. In this scenario, a pathogen propagates within a population of susceptible hosts while a fast mutation process allows its phenotype to change in the same time scale as the invasion process. I will consider a special case where only two phenotypes exists, leading to a system of two coupled KPP-type equations.
I will first talk about the case of a homogeneous space, where the reaction coefficients do not depend on the space variable, and present a construction of traveling waves that allow us to characterize the propagation. Then, I will investigate the case of a periodically heterogeneous space, and show how we constructed pulsating fronts in this situation. In both cases, there is competition between the two pathogens, which we treated as a non-local term ; in particular, we are not in a situation where a comparison principle is available, which is a challenging mathematical problem.

JPEG - 22.5 ko
Quentin GRIETTE

Lieu : CMI, salle de séminaire R164 (1er étage) - I2M - Château-Gombert
39 rue Frédéric Joliot-Curie
13453 Marseille cedex 13

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