Analysis on a diffusive two-stage epidemic model with logistic growth and saturated incidence rates

In this paper, we investigate a two-stage epidemic model with logistic growth and saturated incidence rates in a spatially heterogeneous environment. First, the global existence of the nonnegative solution and the existence of global attractor are proved. Then the basic reproduction number R0 is established as a threshold for the dynamics of the disease with the next generation operator method. It is shown that the disease-free equilibrium is globally attractive if R0<1 and the disease is uniformly persistent if R0>1. Furthermore, we investigate the asymptotic profiles of positive steady states as the diffusion rate of the susceptible population tends to 0 and ∞, respectively. Additionally, numerical examples are carried out to verify the results and reveal the biological significance.