Traveling wave solutions of a diffusive seir epidemic model with nonlinear incidence rate

Abstract

This paper is concerned with the existence and nonexistence of traveling wave solutions of a diffusive SEIR epidemic model with nonlinear incidence rate, which are determined by the basic reproduction number R0 and the minimal wave speed c*. Namely, the system admits a nontrivial traveling wave solution if R0 > 1 and c ≥ c* and then the non-existence of traveling wave solutions of the system is established if R0 > 1 and 0 < c < c*. Especially, using numerical simulation, we give the basic framework of traveling wave solutions of the system.