Periodic traveling waves in a time periodic SEIR model with nonlocal dispersal and delay

Abstract

This paper is mainly dedicated to the periodic traveling waves in a time periodic SEIR model with nonlocal dispersal and delay. The existence and the asymptotic behaviors to periodic traveling waves are obtained, respectively, based on the asymptotic fixed point theorem and analysis techniques because of the missing for parabolic estimates and compactness. Especially, the difficulty of examining asymptotic behaviors to periodic traveling waves at $ \xi\rightarrow +\infty $ for the emergence of nonlocal dispersal is resolved by integral techniques and analysis techniques. Moreover, the nonexistence to periodic traveling waves is established.