Traveling waves of a diffusive SIR epidemic model with a class of nonlinear incidence rates and distributed delay

In this paper, we study the traveling waves of a diffusive SIR epidemic model with a class of nonlinear incidence rates of the form beta S(x,t) integral(h)(0) f(tau)g(I(x,t - tau))d tau. We find that the existence of traveling waves is determined by the basic reproduction number of the corresponding spatial- homogenous delay differential equations and the minimal wave speed. The existence proof is to introduce an auxiliary system and apply Schauder's fixed point theorem. The non- existence of traveling waves is obtained by two- sided Laplace transform. (C) 2014 Elsevier B. V. All rights reserved.