Propagation dynamics for a nonlocal dispersal Kermack-McKendrick epidemic system with exposed class and standard incidence

Abstract

In this paper, we study the existence and asymptotic behavior of traveling wave solutions for a nonlocal dispersal susceptible-exposed-infected-recovered (for short SEIR) model with standard incidence rate. By utilizing a proper iteration technique, Schauder's fixed point theorem and the limiting argument, the existence of traveling wave solutions with wave velocity greater than critical wave velocity c⁎ is established. The main difficulty lies in the boundedness of traveling waves caused by nonlocal diffusion operators. Meanwhile, the non-existence of traveling waves with wave velocity less than c⁎ is derived by using bilateral Laplace transform. Our research provides some new insights for dealing with high-dimensional infectious disease models with nonlocal dispersal.