Research On Reaction-diffusion SIR Model Based On Linear Sources And Saturation Incidence

Human society has always been threatened by infect ious diseases in history,and infectious diseases will have a great impact and harm on the economic development of the society and the physical and mental health of human beings every time.Therefore,in order to minimize the impact and harm of infectious diseases on human beings,it is of great significance to establish mathematical models based on existing infectious diseases.This article mainly studies the reaction diffusion SIR model with saturation incidence and linear sources.The first chapter introduces the development and history of some major infectious diseases at home and abroad.then explains the importance of establishing infectious disease models and the currentstatus of domestic and foreign research,and finally briefly introduces the main work of this article.The second chapter is mainly to explain some definitions,theorems and lemmas that need to be used later.The third chapter mainly uses the method of upper and lower solutions to prove the existence and the boundedness of the reaction-diffusion SIR model with linear sources and saturation incidence as follows,and also proves the explict bounds of(1)in the special case κS=κI=κR and the implict bounds of the following system,The fourth chapter first defines the basic reproduction number R0 and the equilibrium solution(EE)of(2),that is,the non-negative solution of the following equation,After that,some properties of R0 are proved for the conditions that need to be used in Chapter 4.Finally,the consistent persistence of the solution of(2)and the impact of R0 as a threshold on the existence of EE of(2)are proved,and we get that When R0>1,there is at least one EE in(2).The fifth Chapter first gives some preliminary estimates of the solution in(3),and then discusses the asymptoticity of the solution in(3)when we give certain assumptions to ensure the existence of EE in the five cases of κS→0,κI→0,κS→∞,κI→∞ and m→∞.The last Chapter mainly summarizes the conclusions drawn from the above proofs,and concludes that it is conducive to the elimination of diseases when the saturation incidence is sufficiently large and the existence of linear sources improves the persistence of infectious diseases.