Analysis on a diffusive SIRS epidemic model with logistic source and saturated incidence rate

This paper provides the qualitative analysis on a diffusive SIRS epidemic model with logistic source and saturated incidence rate. We first establish uniform boundedness of parabolic system, then explore extinction/persistence infectious disease via basic reproduction number. The effects source, dispersal, saturation, spatial heterogeneity asymptotic behaviors endemic equilibrium are also investigated. Our study show that can not be controlled by limiting dispersal rate large saturation may cause elimination disease.