PDE Seminar (2017/11/24): Mathematical analysis of propagation models arising in evolutionary epidemiology

Date
2017-11-24 15:00 - 2017-11-24 16:00
Place
Faculty of Science Building #4, Room 501
Speaker/Organizer
Quentin Griette (The University of Tokyo)
 
The time and venue of this seminar are different from the usual.

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.