Three Classes Of Sis Epidemic Models With Spontaneous Infection In A Heterogeneous Environment

In this paper,we consider three SIS epidemic reaction-diffusion models with spontaneous infection in a spatially heterogeneous environment,which includes two cases: varying total population or not.In the case of varying total population,We prove the uniform boundedness and existence of the solutions of parabolic equations and the asymptotic behaviors of the solutions of steady-state equations when the population presents the logistic situation.On the other hand,We further analyze the effects of diffusion,advection,saturation and spontaneous infection on the asymptotic behaviors of endemic equilibrium in the case of invariant total population.The results on these new models may provide some implications on disease control and prediction.