We consider a West Nile virus model with nonlocal diffusion and free boundaries, in the form of a cooperative evolution system that can be viewed as a nonlocal version of the free boundary model of Lin and Zhu (2017 J . Math . Biol . 75 1381–1409). The model is a representative of a class of ‘vector-host’ models. We prove that this nonlocal model is well-posed, and its long-time dynamical behaviour is characterised by a spreading-vanishing dichotomy. We also find the criteria that completely determine when spreading and vanishing can happen, revealing some significant differences from the model in Lin and Zhu (2017 J . Math . Biol . 75 1381–1409). It is expected that the nonlocal model here may exhibit accelerated spreading (see remark 1.4 part (c)), a feature contrasting sharply to the corresponding local diffusion model, which has been shown by Wang et al (2019 J . Math . Biol . 79 433–466) to ha...

中文翻译：

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具有非局部扩散和自由边界的西尼罗河病毒模型的分析

我们以合作进化系统的形式考虑了具有非局部扩散和自由边界的西尼罗河病毒模型，该模型可以看作是Lin和Zhu（2017 J. Math。Biol。75 1381– 1409）。该模型是一类“向量-宿主”模型的代表。我们证明了该非局部模型是有条件的，其长期动力学行为的特征是消失的二分法。我们还找到了完全确定何时会发生散布和消失的标准，这揭示了与Lin和Zhu（2017 J. Math。Biol。75 1381-1409）中的模型有一些显着差异。可以预期，此处的非局部模型可能会显示出加速的扩展（请参阅备注1.4（c）部分），该特征与相应的局部扩散模型形成鲜明对比，