In this paper, a spatially heterogeneous SIRI epidemic model with general morbidity is studied, which conforms to the Fokker-Planck type diffusion law. The basic reproduction number 91 0 of the model is introduced, and the threshold dynamics based on 91 0 is discussed. In particular, with the help of elliptic eigenvalue theory, we determine the asymptotic profiles of the endemic equilibrium when the diffusion rate of su...