In this paper, we investigate a reaction–diffusion–advection model with expanding fronts, which models the spatial transmission of West Nile virus (WNv) in a heterogeneous environment. A free boundary problem is formulated and the global existence and uniqueness of the solution is presented. In addition to a classical basic reproduction number, the spatial-temporal basic reproduction number for the model with null Dirichlet boundary condition is introduced and the risk index associated with the virus in spatial setting is defined, and their properties are discussed. Sufficient conditions for the WNv to vanish or spread are given, and the asymptotic behavior of the solution to the free boundary problem when the spreading occurs is established. Our results show that the initial number of infected populations and the expanding capability of the expanding fronts exhibit important impacts on the extinction or persistence of the virus.

中文翻译：

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异质环境中具有平流和扩展前沿的西尼罗河病毒扩散模型

在本文中，我们研究了具有扩展前沿的反应-扩散-平流模型，该模型模拟了西尼罗河病毒 (WNv) 在异质环境中的空间传播。建立了一个自由边界问题，并给出了解的全局存在性和唯一性。除了经典的基本再生数外，还引入了空Dirichlet边界条件模型的时空基本再生数，定义了空间环境下与病毒相关的风险指数，并讨论了它们的性质。给出了WNv消失或扩散的充分条件，建立了扩散发生时自由边界问题解的渐近行为。