Analysis On A Diffusive SIS Epidemic Model With Saturated Incidence Rate And Linear Source In A Heterogeneous Environment

In this paper,we are concerned with two reaction-diffusion SIS epidemic model with saturated incidence rate and linear source in spatially heterogeneous environments.We derive the uniform bounds of parabolic system and study the extinction and persistence of the infectious disease in terms of the basic reproduction number.The existence of the endemic equilibrium(EE)is established when the basic reproduction number is greater than one.The global stability of equilibrium state under spatial homogeneous is obtained.We further investigate the effects of diffusion and saturation on asymptotic profiles of the endemic equilibrium.On the other hand,consider the reaction-diffusion SIS epidemic model with spontaneous infection mechanism.Derive the uniform bounds of parabolic system and prove the global asymptotic stability of the unique positive constant steady state in the case of homogeneous environment.The existence of the positive steady state is established.Finally,analyze the asymptotic profiles of positive steady state when the movement rate of the susceptible and infected is large or small and the saturation rate is large.These results may provide some useful enlightenment for disease prevention and control.