An SIR epidemic model with nonlocal diffusion, nonlocal infection and free boundaries

In this paper, taking into account the long range dispersal, environmental carrying capacity and propagation of viruses in the air, we propose a new SIR epidemic model with nonlocal diffusion, nonlocal infection and free boundaries. We first prove that such a nonlocal problem with free boundaries has a unique global solution. Then find the basic reproduction number R-0(theta/b, (- h(0), h(0))) and show that when R-0(theta/b, (- h(0), h(0))) >= 1the disease will spread; when R-0(theta/b, (- h(0), h(0))) < 1, the disease will spread or not depending on the expanding ability mu of I. Moreover, we give the conditions that determine R-0(theta/b, (- h(0), h(0))) =(>, <) 1, and give the criteria for spreading and vanishing. (c) 2022 Elsevier Inc. All rights reserved.