Traveling Wave Solutions For A Nonlocal Reaction Diffusion Epidemic Model With Time Delay

The spread of infectious diseases will bring great harm to the stability of human society.The research on epidemic model can provide theoretical basis for people to prevent and control epidemic diseases.In this paper,we mainly study the existence and nonexistence of traveling wave solutions for a class of nonlocal reaction diffusion delay epidemic models.The article is divided into five chapters.The first chapter mainly introduces the background and significance of the research on epidemic disease model,as well as the research status at home and abroad,and briefly introduces the main research results and methods used in this article.In the second chapter,an introduction to some of the basic knowledge required for this article and the epidemic model related to this article.In Chapter 3 and Chapter 4,we study the existence and nonexistence of traveling wave solutions for a nonlocal reaction diffusion delay epidemic model.Through the two-side Laplace transform and some integral estimation,a normal number c is obtained.By constructing the auxiliary system,Schauder fixed point theorem,limit theorem,two-side Laplace transform and Fubini theorem,it is proved that when the basic regeneration number Ro and wave velocity c satisfy condition R0>1,c?c*,then there is a traveling wave solution for the delay SIR epidemic model.While R0>1,0<c<c*or R0?1,c>0 are satisfied,then there is no traveling wave solution for the SIR epidemic model with time delay.In Chapter 5,we summarize the research and point out the shortcomings.