一类具有非线性发生率与时滞的非局部扩散SIR模型的行波解

Traveling Waves in a Nonlocal Dispersal SIR Epidemic Model with Delay and Nonlinear Incidence

该文研究了一类具有非线性发生率与时滞的非局部扩散SIR传染病模型的行波解问题.利用基本再生数R_0和最小波速c~*判定行波解的存在与否.首先,当c>c~*,R_0>1时,通过对一个截断问题使用Schauder不动点定理以及取极限的方法证明了所研究模型的行波解的存在性,其次,当0<c<c~*,R_0>1或R_0≤1时,利用双边拉普拉斯变换的性质证明了行波解的不存在性.

This paper is concerned with the traveling waves of a nonlocal dispersal SIR epidemic model with delay and nonlinear incidence. The threshold dynamics are determined by the basic reproduction number R_0 and the minimal wave speed c~＊. First, when c c~＊, R_0 1,the existence of the traveling waves is proved by applying Schauder＇s fixed point theorem and a limiting argument. Then, when 0 c c~＊, R_0 1 or R_0 ≤ 1, the non-existence of traveling wave solutions is established by two-side Laplace transform.