This paper is concerned with the spatial propagation of an SIR epidemic model with nonlocal diffusion and free boundaries describing the evolution of a disease. This model can be viewed as a nonlocal version of the free boundary problem studied by Kim et al. (An SIR epidemic model with free boundary. Nonlinear Anal RWA, 2013, 14: 1992–2001). We first prove that this problem has a unique solution defined for all time, and then we give sufficient conditions for the disease vanishing and spreading. Our result shows that the disease will not spread if the basic reproduction number R₀ < 1, or the initial infected area h₀, expanding ability μ, and the initial datum S₀ are all small enough when \(1 < {R_0} < 1 + {d \over {{\mu _2} + \alpha }}\). Furthermore, we show that if \(1 < {R_0} < 1 + {d \over {{\mu _2} + \alpha }}\), the disease will spread when h₀ is large enough or h₀ is small but μ is large enough. It is expected that the disease will always spread when \({R_0} \ge 1 + {d \over {{\mu _2} + \alpha }}\), which is different from the local model.

本文关注具有非局部扩散和描述疾病演变的自由边界的 SIR 流行模型的空间传播。该模型可以看作是 Kim 等人研究的自由边界问题的非局部版本。（的SIR模型自由边界非线性分析RWA，2013。14：1992- 2001年）。我们首先证明这个问题有一个永远定义的唯一解，然后我们给出了疾病消失和传播的充分条件。我们的结果表明，如果基本繁殖数R ₀ < 1，或初始感染面积h ₀，扩展能力μ和初始数据S ₀，则疾病不会传播当\(1 < {R_0} < 1 + {d \over {{\mu _2} + \alpha }}\)时都足够小。此外，我们表明，如果\(1 < {R_0} < 1 + {d \over {{\mu _2} + \alpha }}\)，当h ₀足够大或h ₀很小但疾病会传播μ足够大。预计疾病总是在\({R_0} \ge 1 + {d \over {{\mu _2} + \alpha }}\)时传播，这与局部模型不同。