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A Gaussian-process approximation to a spatial SIR process using moment closures and emulators
arXiv - STAT - Methodology Pub Date : 2022-08-05 , DOI: arxiv-2208.03157
Parker Trostle, Joseph Guinness, Brian J. Reich

The dynamics that govern disease spread are hard to model because infections are functions of both the underlying pathogen as well as human or animal behavior. This challenge is increased when modeling how diseases spread between different spatial locations. Many proposed spatial epidemiological models require trade-offs to fit, either by abstracting away theoretical spread dynamics, fitting a deterministic model, or by requiring large computational resources for many simulations. We propose an approach that approximates the complex spatial spread dynamics with a Gaussian process. We first propose a flexible spatial extension to the well-known SIR stochastic process, and then we derive a moment-closure approximation to this stochastic process. This moment-closure approximation yields ordinary differential equations for the evolution of the means and covariances of the susceptibles and infectious through time. Because these ODEs are a bottleneck to fitting our model by MCMC, we approximate them using a low-rank emulator. This approximation serves as the basis for our hierarchical model for noisy, underreported counts of new infections by spatial location and time. We demonstrate using our model to conduct inference on simulated infections from the underlying, true spatial SIR jump process. We then apply our method to model counts of new Zika infections in Brazil from late 2015 through early 2016.

中文翻译:

使用矩闭包和仿真器的空间 SIR 过程的高斯过程近似

控制疾病传播的动态很难建模,因为感染既是潜在病原体的功能,也是人类或动物行为的功能。在对疾病如何在不同空间位置之间传播进行建模时,这一挑战会增加。许多提出的空间流行病学模型需要权衡取舍,要么通过抽象出理论传播动力学,拟合确定性模型,要么通过许多模拟需要大量计算资源。我们提出了一种用高斯过程近似复杂空间传播动力学的方法。我们首先提出对众所周知的 SIR 随机过程的灵活空间扩展,然后我们推导出该随机过程的矩闭合近似。这种矩闭合近似产生常微分方程,用于随时间推移易感者和感染者的均值和协方差的演变。因为这些 ODE 是通过 MCMC 拟合我们的模型的瓶颈,所以我们使用低秩仿真器来近似它们。这种近似值是我们的分层模型的基础,该模型用于按空间位置和时间划分的嘈杂、未报告的新感染计数。我们演示了使用我们的模型从潜在的真实空间 SIR 跳跃过程中对模拟感染进行推断。然后,我们将我们的方法应用于模拟 2015 年底至 2016 年初巴西新的寨卡病毒感染人数。这种近似值是我们的分层模型的基础,该模型用于按空间位置和时间划分的嘈杂、未报告的新感染计数。我们演示了使用我们的模型从潜在的真实空间 SIR 跳跃过程中对模拟感染进行推断。然后,我们将我们的方法应用于模拟 2015 年底至 2016 年初巴西新的寨卡病毒感染人数。这种近似值是我们的分层模型的基础,该模型用于按空间位置和时间划分的嘈杂、未报告的新感染计数。我们演示了使用我们的模型从潜在的真实空间 SIR 跳跃过程中对模拟感染进行推断。然后,我们将我们的方法应用于模拟 2015 年底至 2016 年初巴西新的寨卡病毒感染人数。
更新日期:2022-08-08
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