Traveling waves for a nonlocal dispersal SIR model with delay and external supplies

Abstract

This paper is concerned with the existence, nonexistence and minimal wave speed of traveling waves of a nonlocal dispersal delayed SIR model with constant external supplies and Holling-II incidence rate. We find that the existence and nonexistence of traveling waves of the system are not only determined by the minimal wave speed c∗, but also by the so-called basic reproduction number R0 of the corresponding reaction system. That is, we establish the existence of traveling waves for R0>1 and each wave speed c⩾c∗, and the nonexistence for R0>1 and any 0<c<c∗ or R0<1. We also discuss how the latency of infection and the spatial movement of the infective individuals affect the minimal wave speed. Biologically speaking, the longer the latency of infection in a vector is, the slower the disease spreads.