Abstract

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 R0(θ/b,(−h0,h0)) and show that when R0(θ/b,(−h0,h0))≥1 the disease will spread; when R0(θ/b,(−h0,h0))<1, the disease will spread or not depending on the expanding ability μ of I. Moreover, we give the conditions that determine R0(θ/b,(−h0,h0))=(>,<)1, and give the criteria for spreading and vanishing.

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