A nonlocal diffusion SIR epidemic model with nonlocal incidence rate and
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.