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 $R_0$ and the minimal wave speed $c^*$. Namely, the system admits a nontrivial traveling wave solution if $R_0 \gt 1$ and $c \geq c^*$ and then the non-existence of traveling wave solutions of the system is established if $R_0 \gt 1$ and $0 \lt c \lt c^*$. Especially, using numerical simulation, we give the basic framework of traveling wave solutions of the system.