偏微分方程式セミナー(2017/11/24): Mathematical analysis of propagation models arising in evolutionary epidemiology

開催日時
2017年   11月 24日 15時 00分 ~ 2017年   11月 24日 16時 00分
場所
北海道大学理学部4号館4-501室
講演者
Quentin Griette 氏 (東京大学)
 
開始時刻と会場が通常と異なります.

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.

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