The Study Of The Dynamical Behaviors Of A Class Of SIS Epidemic Model

Spatial heterogeneity,connectivity between places of residence,and migration of individuals can have a significant impact on the persistence and extinction of disease.In order to study these important factors affecting the spread of the disease,in this paper,we consider a class of SIS epidemic patch model.By using the properties of irreducible matrices,we study an equivalent system of the SIS patch model,and then consider the asymptotic behaviors of the endemic equilibrium.The contents of this paper are as follows:In chapter 1,we introduce the research background,domestic and foreign research status and the main work of this paper.In chapter 2,we focus on the case of when there exist both high risk patches and low risk patches,without medium risk patches.Firstly,we study the asymptotic behaviors of the endemic equilibrium when the diffusion coefficients of the susceptible and the infected individuals tend to infinity,and then study the asymptotic behaviors of the endemic equilibrium of the system when the diffusion coefficient of diseased individuals tends to zero.Finally,we use the numerical simulations to verify our analytical results.In chapter 3,we consider the case of when there exist both high risk patches and medium risk patches,without low risk patches.We study the asymptotic behaviors of the endemic equilibrium of the system when the diffusion coefficient(susceptible and the infected individuals)approaches zero.The numerical simulation supports the theoretical results.In chapter 4,we consider the case of when there exist both high risk patches,medium risk patches and low risk patches.We study the asymptotic behaviors of the endemic equilibrium solution of the system when the diffusion coefficient of the susceptible and infected individuals tends to zero.Finally,we carried out numerical simulations.The results in this paper show that,in heterogeneous space environment,reasonable restrictions on the migration of individuals,or controling the path of individual migration is effective for the prevention of disease spread.These results are important for predicting disease patterns and developing optimal disease control strategies.