Traveling wave solutions for a SEIR epidemic model in combination with random dispersal and nonlocal dispersal

Abstract

This paper is devoted to the existence and nonexistence of traveling wave solutions for an SEIR model in combination with random dispersal and nonlocal dispersal, which can be seen as a continuity work of Tian and Yuan (16). The main difficulties lie in the fact that the semiflow generated by the model does not have the order-preserving property and the solutions lack of regularity. We use a proper iteration technique to construct a pair of upper and lower solutions, find a new nonmonotone operator and then apply Schauder fixed point theorem to obtain the threshold dynamics for this model. Our results also show that the diffusion ability of the exposed individuals and the infected individuals can accelerate the speed of the spread of the disease while the nonlocal interaction between the infective and the susceptible individuals can speed up the spread of the disease.