Analysis on a Diffusive SIS Epidemic Model in an Asymptotically Bounded Domain

To examine the effect of evolving domain on the spread and control of disease, we study an SIS reaction-diffusion model with Dirichlet boundary conditions in an asymptotically bounded domain. Firstly, the basic reproduction number R-0 is defined, which relies on the evolution rate of the domain, the diffusion rate of infected individuals and spatial heterogeneity. We analyze the asymptotic stability of the disease-free equilibrium by the sub-solution and super-solution method and energy-estimates. Secondly, the existence and uniqueness, as well as the global stability of the endemic equilibrium in a special case are investigated. Finally, we discuss the asymptotic profiles of the endemic equilibrium for small and large diffusion rates of the susceptible individuals and the infected individuals. Numerical simulations are performed to illustrate the analytical results.