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Bayesian inference of heterogeneous epidemic models: Application to COVID-19 spread accounting for long-term care facilities
Computer Methods in Applied Mechanics and Engineering ( IF 7.2 ) Pub Date : 2021-07-03 , DOI: 10.1016/j.cma.2021.114020
Peng Chen 1 , Keyi Wu 2 , Omar Ghattas 1, 3
Affiliation  

We propose a high dimensional Bayesian inference framework for learning heterogeneous dynamics of a COVID-19 model, with a specific application to the dynamics and severity of COVID-19 inside and outside long-term care (LTC) facilities. We develop a heterogeneous compartmental model that accounts for the heterogeneity of the time-varying spread and severity of COVID-19 inside and outside LTC facilities, which is characterized by time-dependent stochastic processes and time-independent parameters in 1500 dimensions after discretization. To infer these parameters, we use reported data on the number of confirmed, hospitalized, and deceased cases with suitable post-processing in both a deterministic inversion approach with appropriate regularization as a first step, followed by Bayesian inversion with proper prior distributions. To address the curse of dimensionality and the ill-posedness of the high-dimensional inference problem, we propose use of a dimension-independent projected Stein variational gradient descent method, and demonstrate the intrinsic low-dimensionality of the inverse problem. We present inference results with quantified uncertainties for both New Jersey and Texas, which experienced different epidemic phases and patterns. Moreover, we also present forecasting and validation results based on the empirical posterior samples of our inference for the future trajectory of COVID-19.



中文翻译:

异质流行病模型的贝叶斯推断:在长期护理机构的 COVID-19 传播核算中的应用

我们提出了一个高维贝叶斯推理框架,用于学习 COVID-19 模型的异构动力学,具体应用于长期护理 (LTC) 设施内外 COVID-19 的动力学和严重性。我们开发了一个异质隔间模型,该模型解释了 LTC 设施内外 COVID-19 的时变传播和严重性的异质性,其特点是时间相关的随机过程和时间无关的参数~离散化后的 1500 个维度。为了推断这些参数,我们使用关于确诊、住院和死亡病例数量的报告数据,并在确定性反演方法和适当正则化作为第一步的确定性反演方法中进行适当的后处理,然后使用适当的先验分布进行贝叶斯反演。为了解决维数灾难和高维推理问题的不适定性,我们提出使用维数无关的投影斯坦因变分梯度下降法,并证明了逆问题的内在低维性。我们为经历了不同流行阶段和模式的新泽西州和德克萨斯州提供了具有量化不确定性的推理结果。而且,

更新日期:2021-07-12
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