Traveling waves for a diffusive SEIR epidemic model with non-local reaction

Abstract This paper is devoted to the existence of the traveling waves of the equations describing a diffusive SEIR model with non-local reaction between the infected and the susceptible. The existence of traveling waves depends on the basic reproduction rate S − ∞ β / γ and the minimal speed. We use the Schauder fixed point theorem and the Laplace transform to get the existence and non-existence of traveling waves in our paper. We also give some numerical results of the minimal wave speed.