Traveling wave solutions for a nonlocal dispersal Kermack-McKendrick epidemic model with spatio-temporal delay

This paper mainly discusses the existence and non-existence of traveling wave solutions for the nonlocal Kermack-McKendrick epidemic model with nonlocal delayed transmission. We get that the existence and non-existence of traveling wave solutions are determined by the reproduction number and the wave speed. We also obtain that the spreading speed of the traveling wave solutions depends on the nonlocal delayed interaction and spatial movement patterns of the individuals. To prove these results, we apply the Schauders xed point theorem and the properties of Laplace transform.