Dynamics and calculation of the basic reproduction number for a nonlocal dispersal epidemic model with air pollution.

Abstract

In order to reflect the dispersal of pollutants in non-adjacent areas and the large-scale movement of individuals, this paper proposes an epidemic model of nonlocal dispersal with air pollution, where the transmission rate is related to the concentration of pollutants. This paper checks the uniqueness and existence of the global positive solution and defines the basic reproduction number, . We simultaneously explore the global dynamics: when , the disease-free stable point is global asymptotic stability; when , the disease is uniformly persistent. Additionally, in order to approximate , a numerical method has been introduced. Illustrative examples are used to verify the theoretical outcomes and show the effect of the dispersal rate on the basic reproduction number .