Steady-state Solutions Of Nonhomogeneous Region Of SIRS Epidemic Model

The epidemic model is a study of the pathogenesis and spread of infectious diseases between individuals and regions.By using some appropriate hypotheses,the mathemat-ical factors that can determine the process of transmission of infectious diseases are transformed into the relevant mathematical variables in the mathematical model.The dynamics theory is used to analyze the development trend of the disease so as to help us to predict and control the disease in life.The number of regenerations is an important threshold parameter in an infectious disease model,the number of patients transmit-ted in an average prevalence period,and the number of basic regenerations determines whether the disease spreads or subsides,but we are increasingly aware of the spatial diffusion and environmental heterogeneity Sex is not only an important factor affecting the regression and spread of the disease,but also determines the mode of transmission and transmission of the disease,so that the basic basic regeneration is not enough to describe the spread of the disease,nor does it reflect the spatial characteristics of the study area.It is necessary to study the role of proliferation in the spread and control of disease in the region.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 R₀^N of the reaction diffusion problem with homogeneous Neumann boundary condition.On this basis,The basic reproduction number R₀^D of the reaction diffusion problem with homogeneous Dirichlet boundary condition is defined by the boundary,and the basic regeneration number R₀^F?t?of the SIS model with free boundary is introduced.And discussed the regression and spread of the disease.In this paper,we use a new non-homogeneous SIRS 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 ef-fect 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 ex-istence 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 SIRS epidemic model,given in section 2 recent research status;The second chapter gives the Lyapunov stability in the first quarter,second quarter giv-en 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 SIRS 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 of this paper makes relevant research summary.