Some results on an evolutionary-epidemic problem arising in plant disease
周五公众报告
报告题目(Title)：Some results on an evolutionary-epidemic problem arising in plant disease
报告人(Speaker)：Arnaud Ducrot (University of Le Havre, France)
地点(Place)：后主楼1124室
时间(Time)：2019年4月19日15:00-16:00
邀请人(Inviter)：刘志华
报告摘要
In this talk we discuss various properties of an evolutionary-epidemic system modelling plant disease epidemic and incorporating the ability of the pathogen to adapt to the environment by mutation. The resulting problem consists in an intregro-differential system of equations that typically depends on a small parameter $\varepsilon>0$ that describes a mutation parameter.
In a first part of this talk, we show that the system asymptotically stabilizes toward its unique endemic equilibrium and we describe, using the small parameter $\varepsilon$, a possibly long transient behaviour before reaching the equilibrium.
In a second time, the above problem is extended to the case where the populations are also structured with respect to space and where the infection is able to disperse. In that setting, we discuss the spatio-temporal evolution of the disease by studying some properties of the travelling wave solutions for this system modelling the spatial invasion of the disease.
