This work proposes and analyzes a family of spatially inhomogeneous epidemic models. This is our first effort to use stochastic partial differential equations (SPDEs) to model epidemic dynamics with spatial variations and environmental noise. After setting up the problem, the existence and uniqueness of solutions of the underlying SPDEs are examined. Then, definitions of permanence and extinction are given, and certain sufficient conditions are provided for permanence and extinction. Our hope is that this paper will open up windows for investigation of epidemic models from a new angle.

中文翻译：

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空间非齐次随机偏微分方程流行病模型分析

这项工作提出并分析了一系列空间不均匀的流行病模型。这是我们第一次尝试使用随机偏微分方程 (SPDE) 来模拟具有空间变化和环境噪声的流行病动态。设置问题后，检查底层 SPDE 解的存在性和唯一性。然后，给出了恒灭的定义，并为恒灭提供了一定的充分条件。我们希望这篇论文能够从一个新的角度为流行病模型的研究打开窗口。