A nonlocal SIS epidemic problem with double free boundaries

Abstract

In this paper, we investigate a nonlocal SIS epidemic model with double free boundaries. The existence, uniqueness and some estimates of the global solution are discussed first. Then, with the help of studying the long-time behavior of the solution to a Cauchy problem for a nonhomogeneous heat equation, the long-time behavior of the solution to the SIS free boundary problem is obtained for the disease vanishing case. At last, some sufficient conditions for the disease vanishing are established.