Study On The Steady-state Solutions Of The Reaction-diffusion Epidemic Models

In this thesis,we study the existence and stability of the steadystate solutions of the reaction-diffusion epidemic models.There are four chapters in this thesis.In the first chapter,this paper expounds the research overview of reaction diffusion epidemic model.The main problems involved in this paper are also described briefly.In the second chapter,we study the steady-state solution of reaction diffusion model with direct transmission.We first give a prior estimates of upper and lower bounds for positive solutions to model,and then give the conditions of the existence and non-existence of the positive non-constant steady states.In the third chapter,We investigate the disease dynamics of a reactiondiffusion model incorporating direct and indirect transmissions as well as spatially environment heterogeneity,and we give the definition of the basic reproductive number.In the fourth chapter,we summarize the paper.