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

TL;DR

This paper presents a novel metric geometry-based method to analyze the spatial spread of COVID-19 in the US, revealing key periods of geographic shift and patterns of reversion in epidemic distribution.

Contribution

It introduces a geodesic Wasserstein metric approach for spatio-temporal analysis, providing new insights into epidemic propagation and spatial reversion patterns.

Findings

Major geographic shift in COVID-19 spread between May and June 2020

COVID-19 distribution was most concentrated in May 2020

Identified patterns of spatial reversion across different waves

Abstract

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.