We consider an epidemic model with nonlocal diffusion and free boundaries, which describes the evolution of an infectious agents with nonlocal diffusion and the infected humans without diffusion, where humans get infected by the agents, and infected humans in return contribute to the growth of the agents. The model can be viewed as a nonlocal version of the free boundary model studied by Ahn, Beak and Lin \cite{ABL2016}, with its origin tracing back to Capasso et al. \cite{CP1979, CM1981}. We prove that the problem has a unique solution defined for all $t>0$, and its long-time dynamical behaviour is governed by a spreading-vanishing dichotomy. Sharp criteria for spreading and vanishing are also obtained, which reveal significant differences from the local diffusion model in \cite{ABL2016}. Depending on the choice of the kernel function in the nonlocal diffusion operator, it is expected that the nonlocal model here may have accelerated spreading, which would contrast sharply to the model of \cite{ABL2016}, where the spreading has finite speed whenever spreading happens \cite{ZLN2019}.

中文翻译：

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具有非局部扩散和自由边界的退化流行模型的动力学

我们考虑一个具有非局部扩散和自由边界的流行病模型，它描述了具有非局部扩散的传染性病原体和没有扩散的受感染人类的​​进化，其中人类被病原体感染，而受感染的人类反过来又促进了病原体的生长. 该模型可以看作是 Ahn、Beak 和 Lin \cite{ABL2016} 研究的自由边界模型的非局部版本，其起源可以追溯到 Capasso 等人。\cite{CP1979，CM1981}。我们证明该问题具有为所有 $t>0$ 定义的唯一解决方案，并且其长期动态行为受传播-消失二分法支配。还获得了扩散和消失的清晰标准，这揭示了与 \cite{ABL2016} 中的局部扩散模型的显着差异。