A nonlocal diffusion SIR epidemic model with nonlocal incidence rate and free boundaries

Abstract

This paper is concerned with the spreading or vanishing of an epidemic disease which is characterized by a nonlocal diffusion SIR model with nonlocal incidence rate and double free boundaries. We prove that the disease will vanish if the basic reproduction number , or the initial area , the initial datum , and the expanding ability are sufficiently small when . Otherwise, the disease will spread to the whole area if , when is suitably large or is small but is large enough. Moreover, we also show the long‐time asymptotic limit of the solution when vanishing happens.