Traveling waves of a diffusive SIR epidemic model with general nonlinear incidence and infinitely distributed latency but without demography

Abstract

In this paper, we are concerned with existence/non-existence of traveling waves of a diffusive SIR epidemic model with general incidence rate of the form of f(S)g(I) and infinitely distributed latency but without demography. We show that the existence of traveling waves only depends on the basic reproduction number of the corresponding spatial-homogeneous system of delay differential equations, which is determined by the recovery rate, the local properties of f and g and a minimal wave speed c∗ that is affected by the distributed delay. The proof of existence of traveling waves is by employing Schauder’s fixed point theorem, and the proof of nonexistence is completed with the aid of the bilateral Laplace transform.