An SIR epidemic model with nonlocal diffusion and free boundaries

In this short paper, based on the long range dispersal and environmental carrying capacity, we propose a new SIR epidemic model discuss its dynamic properties. The results show that disease will always spread if basic reproduction number $ \mathcal{R}_0(\theta/b,\,(-h_0,h_0))\ge 1 $; however, when \mathcal{R}_0(\theta/b,\,(-h_0,h_0))<1 $, whether spreading or vanishing depends expansion ability \mu of I $.