Analysis Of Infectious Diseases Model With Reaction-diffusion

At present,many infectious diseases are still endangering the survival and development of human beings.Therefore,it is of crucial significance and practical value to use the knowledge of the epidemic dynamics to establish the mathematical model of infectious diseases and study the threshold dynamic behavior of infectious disease model and Hopf branch of infectious disease model,which makes us obtain the spread law of infectious diseases,analyzing how factors such as infectious disease transmission route and infection mode affect the transmission of diseases.This paper focuses on two types of infectious disease models with reactive diffusion,as follows:1.The threshold dynamics and hopf branching problems of a reaction-diffusion hostpathogen model with horizontal transmission is analyzed.Firstly,the method of Young's inequality and divergence theorem was used to study the suitability of the model,that is,the positivity and boundedness of the solution of the system with initial boundary value condition;then,we give the threshold dynamics for extinction and persistence of the disease in terms of basic reproduction number.Finally,we carry out a bifurcation analysis for steady state solutions.2.The threshold dynamics of a class of reaction-diffusion HBV models was studied.First,we give the well-posedness of the model,That is,the global existence of solutions and the uniform boundedness of solutions,and by introducing Kuratowski measure of noncompactness,the asymptotic smoothness of semi-flow is given.Then,we give the threshold dynamics for extinction and persistence of the disease in terms of basic reproduction number.