Qualitative Analysis on a Reaction–Diffusion SEAIR Model With Logistic Growth and Saturated Incidence Rates

ABSTRACT In this paper, a SEAIR epidemic model with saturated incidence in a spatially heterogeneous environment is investigated. Firstly, by defining a noncompact measure, the well‐posedness including the global existence of the nonnegative solution and the existence of the global attractor are established. Then, using the next generation operator method, the basic reproduction number is given as the threshold of disease dynamics. Some properties about basic reproduction number are also given. The result of the threshold dynamics shows that the disease‐free equilibrium is globally asymptotically stable for , while the disease is uniformly persistent for . Additionally, with the diffusion rate of the susceptible population tending to 0 and , the asymptotic profiles of positive steady states are investigated. Finally, through numerical examples, the research results are verified and biological significance is revealed.