Dynamics of a nonlocal SEIR model with free boundaries

This paper investigates the dynamics of a nonlocal SEIR epidemic model with free boundaries. We focus on a comprehensive analysis of disease dynamics governed by both nonlocal diffusion and expanding habitat. A spreading-vanishing criterion is established by comparing the basic reproduction number [Formula: see text] with unity, as well as some conclusions that determine whether the disease vanishes or spreads. Our analysis underscores the critical role of free boundaries: in addition to the basic reproduction number [Formula: see text], the initial values of the infected and exposed populations, and the spatial diffusivity of the disease in a new region also exert significant influence on disease transmission. These observations highlight one of the key distinctions between fixed boundary and free boundary problems. Furthermore, we carry out numerical simulations to validate our theoretical results.