TRAVELING WAVES FOR A DIFFUSIVE SEIR EPIDEMIC MODEL

摘要

this paper, we propose a diffusive SEIR epidemic model with saturating incidence rate. We first study the well posedness of the model, and give the explicit formula of the basic reproduction number R-0. And hence, we show that if R-0 > 1, then there exists a positive constant c* > 0 such that for each c > c*, the model admits a nontrivial traveling wave solution, and if R-0 <= 1 and c >= 0 (or, R-0 > 1 and c epsilon [0, c*)), then the model has no nontrivial traveling wave solutions. Consequently, we confirm that the constant c* is indeed the minimal wave speed. The proof of the main results is mainly based on Schauder fixed theorem and Laplace transform.