Traveling Waves For A Two-group Epidemic Model With Latent Period In A Patchy Environment

This paper is concerned with the existence and nonexistence of traveling waves of a two-group epidemic model with latent period in a patchy environment.The paper consists of the following four chapters.In chapter 1,firstly we introduce the background and the development of the epidemic model,secondly we introduce the main results of our paper.In chapter 2,we derive our model by applying discrete Fourier transform.In chapter 3,firstly we introduce a pair of upper and lower solutions of the system and construct an invariant cone.Then we build a continuous and compact operator.By using Schauder’s fixed point theorem,we prove that when the basic reproduction numberR₀（S₁⁰,S₀²）> 1 and c > c^*,the system admits a nontrivial traveling wave solution.At last we show that there is no nontrivial traveling waves satisfying ψ_i（±∞）= 0,φ_i（-∞）=S_i⁰,i= 1,2,when R₀（S₁⁰,S₀²）≤ 1 and c > 0 by a contradiction argument.In chapter 4,we discuss the unsolved problem of the paper,and simply introduce the interested problems we will focus on.