Research On The Dynamic Behavior Of Reaction-diffusion Infectious Disease Models In Several Heterogeneous Environments

Qualitative and quantitative analysis of dynamics of infectious disease model is an important method to study the law of infectious disease transmission.In this paper,we study the dynamic behavior of reaction-diffusion infectious disease models with homogeneous Neumann boundary conditions in heterogeneous environments.In the aspect of model formulation,we focus on the following points,1)Birth and death of population,the total population of the model is not conserved.2)Spatial heterogeneity,all epidemiological parameters of the model are functions of spatial location,not constants.3)Individual mobility,susceptible and infected individuals can move throughout the habitat.4)Spontaneous infection mechanism,susceptible person transforms into the infected person in a certain way.In mathematical analysis,we prove the uniform boundedness of solution;the global stability of the endemic steady state under homogeneous space,the existence of endemic steady state in spatially heterogeneous environment.Finally,we investigate the asymptotical profiles of the endemic steady state as the dispersal rate of the susceptible or infected hosts approaches zero or infinite.Mathematical results reveal that no matter the diffusion rate of susceptible and infected people approaches zero or infinite,the disease will always persist.