  This paper is concerned with a nonlocal dispersal
susceptible-infected-susceptible (SIS) epidemic model with Dirichlet boundary
condition, where the rates of disease transmission and recovery are assumed to
be spatially heterogeneous. We introduce a basic reproduction number $R_0$ and
establish threshold-type results on the global dynamic in terms of $R_0$. More
specifically, we show that if the basic reproduction number is less than one,
then the disease will be extinct, and if the basic reproduction number is
larger than one, then the disease will persist. Particularly, our results imply
that the nonlocal dispersal of the infected individuals may suppress the spread
of the disease even though in a high-risk domain.
