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 R 0 < 1 , or the initial area h 0 , the initial datum S 0 , and the expanding ability µ are sufficiently small even that R 0 > 1 , and the disease will spread to the whole area if R 0 > 1 , when h 0 is suitably large or h 0 is small but µ is large enough. Moreover, we also show that the long-time asymptotic limit of the solution when vanishing happens.