带有非局部扩散项和时空时滞的Kermack-McKendrick传染病模型的行波解

Traveling wave solutions for a nonlocal dispersal KermackMc Kendrick epidemic model with spatio-temporal delay

本文主要考虑带有非局部扩散项和反应项的Kermack-Mc Kendrick传染病模型的行波解的存在性问题,得出行波解的存在性不仅与基本再生数有关,还与波速有关.同时,还可以得到行波解的移动速度依赖于个体之间的相互作用以及个体的空间运动.利用Schauder不动点定理得到行波解的存在性,利用Laplace变换的性质得到行波解的不存在性.

This paper mainly discusses the existence and non-existence of traveling wave solutions for the nonlocal Kermack-McKendrick epidemic model with nonlocal delayed transmission. We get that the existence and non-existence of traveling wave solutions are determined by the reproduction number and the wave speed. We also obtain that the spreading speed of the traveling wave solutions depends on the nonlocal delayed interaction and spatial movement patterns of the individuals. To prove these results, we apply the Schauder＇s fixed point theorem and the properties of Laplace transform.