Traveling waves in an seir epidemic model with the variable total population

Abstract

In the present paper, we propose a simple diffusive SEIR epidemic model where the total population is variable. We first give the explicit formula of the basic reproduction number R0 for the model. And hence, we show that if R0 > 1, then there exists a constant cΔ > 0 such that for any c > c∗, the model admits a nontrivial traveling wave solution, and if R0 < 1 and c > 0 (or, R0 > 1 and c ϵ (0; c∗)), then the model has no nontrivial traveling wave solution. Consequently, we obtain the full information about the existence and non-existence of traveling wave solutions of the model by determined by the constants R0 and cΔ. The proof of the main results is mainly based on Schauder fixed point theorem and Laplace transform.