Traveling waves of a nonlocal dispersal Kermack-McKendrick epidemic model with delayed transmission

摘要

In this paper, we obtain the information about the existence and nonexistence of traveling waves for the nonlocal Kermack-McKendrick epidemic model with delayed transmission. We find that the information is also determined by the reproduction number and the wave speed is explicitly effected by the delay. To prove these results, we apply the Schauder's fixed point theorem and two-sided Laplace transform. Here, the compactness of the supported set of dispersal kernel is needed in the proof of the existence of the traveling waves.