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arXiv 2108.02516physics.soc-ph
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利用度量几何学理解空间传播及其在美国COVID-19传播中的应用

Understanding spatial propagation using metric geometry with application to the spread of COVID-19 in the United States

Nick James, Max Menzies, Howard Bondell

摘要:

本文介绍了一种使用度量几何进行时空数据分析的新方法,以研究COVID-19在美国的传播。使用测地线Wasserstein度量,我们分析的密度函数之间的差异,新的情况下计数在任何给定的一天,将地理传播的情况下。首先,我们应用这一点来识别COVID-19地理分布变化最深刻的时期。最大的转变发生在2020年5月至6月,当时COVID-19从主要控制东北部各州转变为全国范围内的更广泛分布。我们以分布的测地方差程度的新量度支持我们的发现,证明COVID-19的地理印记最集中于二零二零年五月。接下来,我们研究了这种流行病是否表现出有意义的空间逆转模式,即类似的地理分布稍后会恢复。我们发现,COVID-19在美国的第二波和第三波传播之间存在广泛的相似性,在较小程度上,第一波东北部主导地位的重新出现更接近今天。这种方法可以为分析人员提供新的见解,以监测流行病的动态传播,并使区域决策者能够保护他们的地方。更广泛地说,我们介绍的框架可以应用于随着时间和空间的变化而变化的各种问题。

英文摘要:

This paper introduces a novel approach to spatio-temporal data analysis using metric geometry to study the propagation of COVID-19 across the United States. Using a geodesic Wasserstein metric, we analyse discrepancies between the density functions of new case counts on any given day, incorporating the geographic spread of cases. First, we apply this to identify the periods during which the changes in the geographic distribution of COVID-19 were most profound. The greatest shift occurred between May and June of 2020, when COVID-19 shifted from mostly dominating the Northeastern states to a wider distribution across the country. We support our findings with a new measure of the extent of geodesic variance of a distribution, demonstrating that the geographic imprint of COVID-19 was most concentrated in May 2020. Next, we investigate whether the epidemic exhibited meaningful patterns of spatial reversion, where similar geographic distributions return later. We identify broad similarity between the spread of COVID-19 across the US between the second and third waves, and to a lesser extent, the reemergence of the first wave's Northeastern dominance closer to the present day. This methodology could provide new insights for analysts to monitor the dynamical spread of epidemics and enable regional policymakers to protect their localities. More broadly, the framework we introduce could be applied to a variety of problems evolving over space and time.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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