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

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, [Formula: see text] . We simultaneously explore the global dynamics: when [Formula: see text] , the disease-free stable point is global asymptotic stability; when [Formula: see text] , the disease is uniformly persistent. Additionally, in order to approximate [Formula: see text] , 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 [Formula: see text] .