We extend the classical SIR model of infectious disease spread to account for time dependence in the parameters, which also include diffusivities. The temporal dependence accounts for the changing characteristics of testing, quarantine and treatment protocols, while diffusivity incorporates a mobile population. This model has been applied to data on the evolution of the COVID-19 pandemic in the US state of Michigan. For system inference, we use recent advances; specifically our framework for Variational System Identification (Wang et al. in Comput Methods Appl Mech Eng 356:44–74, 2019; arXiv:2001.04816 [cs.CE]) as well as Bayesian machine learning methods.

中文翻译：

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传染病时空演变的系统推断：COVID-19 时代的密歇根

我们扩展了传染病传播的经典 SIR 模型，以考虑参数的时间依赖性，其中还包括扩散性。时间依赖性解释了检测、隔离和治疗方案的特征变化，而扩散性则包含了流动人口。该模型已应用于美国密歇根州 COVID-19 大流行演变的数据。对于系统推理，我们使用最新进展；特别是我们的变分系统识别框架（Wang et al. in Comput Methods Appl Mech Eng 356:44–74, 2019; arXiv:2001.04816 [cs.CE]）以及贝叶斯机器学习方法。