The Study Of The Solution Of The Elliptic Equations In The Epidemiology Of Infectious Diseases

The serious threat to human health caused by infectious diseases has led to a great deal of research on the cloning,sequencing and genetic evolution of the genome,and the establishment and analysis of the corresponding mathematical models have also been widely concerned.The classical compartment model describes the spread of in-fectious diseases by ordinary differential system.In general,the basic reproductive number determines whether the disease is spreading or subsiding.But in recent years,it is gradually realized that spatial heterogeneity and environmental heterogeneity are not only important factors affecting the regression and spread of diseases,but also de-termine the way and speed of disease transmission.So,usually the basic reproduction number sense is not enough to describe the spread of disease.Accompanied by these requirements,Y Lou was able to analyze the stability of the SIS epidemic model under a heterogeneous region in a timely manner.In this paper,we discuss the stability of the disease-free equilibrium point and the equilibrium point of the disease by defining the basic regeneration number R0N of the reaction diffusion problem with homogeneous Neumann boundary condition.On this basis,The basic reproduction number R0D of the reaction diffusion problem with homogeneous Dirichlet boundary condition is defined by the boundary,and the basic regeneration number R0F(t)of the SIS model with free boundary is introduced.And discussed the regression and spread of the disease.This paper mainly analyzes several models of infectious diseases.The first model is a non homogeneous SI infectious disease model,the basic idea is to construct the basic regeneration number of the model with Neumann boundary condition,and discuss the diffusion of infectious disease to the basic The effect of the number of regenerations R0,that is,if R0<1,the disease-free equilibrium point is globally asymptotically stable if R0>1,Then the disease-free equilibrium is unstable.Therefore,in the low-risk area,we use the bifurcation theory to study the existence and stability of the diseased diseased point.The final results show that reducing the spread of infected patients is not conducive to the elimination of infectious diseases,But the instability of the diseased diseased point indicates that the infectious disease can be controlled.In this paper,the first chapter is the introduction of the first section introduces the background source of SI epidemic model,given in section 2 recent research status;The second chapter gives the Lyapunov stability in the first quarter,second quarter given Crandall-Rabinowitz bifurcation theory of knowledge,the third section gives local bifurcation images and the related knowledge of the principles of stability of transfor-mation;The third chapter discusses the research of SI reaction diffusion model of in-fectious diseases by the definition and characteristics of the basic reproductive number The stability of the disease-free equilibrium infected existence and stability of equilib-ria and the direction of local bifurcation image.The fourth chapter discusses the similar properties of the SIV epidemic model.The fifth chapter discusses the related properties of SIS epidemic model with convection term.The sixth chapter discusses the related properties of the SEIS epidemic model with diffusion term,and the seventh chapter summarizes the research in this paper.