Traveling waves in a Kermack-Mckendrick epidemic model with diffusion and latent period

This paper is devoted to the study of a Kermack-Mckendrick epidemic model with diffusion and latent period. We first consider the well-posedness of solutions of the model. Furthermore, using the Schauder fixed point theorem and Laplace transform, we show that if the threshold value R-0 > 1, then there exists c* > 0 such that for every c > c*, the model admits a traveling wave solution, and if R-0 < 1 and c >= 0; or R-0 > 1 and c is an element of(0, c*), then the model admits no traveling wave solutions. Hence, the existence and nonexistence of traveling wave solutions is determined completely by R-0, and the constant c* is the minimum speed for the existence of traveling wave solutions of the model. (C) 2014 Elsevier Ltd. All rights reserved.