Dynamic Study Of Infectious Disease Model With Spatial Heterogeneity And Spread

In this paper,we study the long term dynamical behavior of a reaction-diffusion cholera epidemic model under Neumann boundary conditions.In the aspect of model formulation,we focus on:1)Spatial heterogeneity（the epidemiological parameter-s of the model are functions that depend on spatial variables,not constants）;2)Different diffusion parameters:Susceptible and infected individuals have different diffusion parameters,while cholera pathogens do not spread;3)Bilinear incidence:disease transmission between susceptibles,infectives and cholere pathogens are de-scribed by mass action law.In the mathematical analysis,we prove the existence of global solutions,uniform boundedness of solution and asymptotic smoothness of semiflows and existence of global attractor.We then identify the basic reproduction number R₀ for the model and prove its to be threshold role.Finally,we investigate the asymptotical profiles of the endemic steady state as the dispersal rate of the sus-ceptible or infected hosts approaches zero.Mathematical results reveal that when the spread rate of the infected person tends to zero,then the individual will gather in the local area of space.