Analysis and visualization of epidemics on the timescale of burden: derivation and application of Epidemic Resistance Lines (ERLs) to COVID-19 outbreaks in the US
Authors: Washburne Alex , Silverman Justin , Lourenco Jose , Hupert Nathaniel 
Published: May 2021

AbstractThe 2020 COVID-19 pandemic produced thousands of well-quantified epidemics in counties, states, and countries around the world. Comparing the dynamics and outcomes of these nested epidemics could improve our understanding of the efficacy of non-pharmaceutical interventions (NPIs) and help managers with risk assessment across multiple geographic levels. However, cross-outbreak comparisons are challenging due to their variable dates of introduction of the SARS-CoV-2 virus, rates of transmission, case detection rates, and asynchronous and diverse management interventions.Here, we present a graphical method for comparing ongoing COVID-19 epidemics by using disease burden as a natural timescale for comparison. Trajectories of growth rates of cases over the timescale of lagged deaths per-capita produces coherent visual comparisons of epidemics that are otherwise incoherent and asynchronous in the timescale of calendar dates or incomparable using non-stationary measures of burden such as cases. Applied to US COVID-19 outbreaks at the county and state level, this approach reveals lockdowns reducing transmission at fewer deaths per-capita early in the epidemic, reopenings causing resurgent summer epidemics, and peaks that while separated in time and place actually occur at points of similar per-capita deaths.Our method uses early and minimally mitigated epidemics, like that in NYC in March-April 2020 and Sweden in later 2020, to define what we call “epidemic resistance lines” (ERLs) or hypothesized upper bounds of epidemic speed and burden. ERLs from less-mitigated epidemics allow benchmarking of resurgent summer epidemics in the US. In particular, the unmitigated NYC epidemic resistance line appears to bound the growth rates of 3,000 US counties and funnel growth rates across counties to their peaks where growth rates equal zero in the fall and winter of 2020. Corroboration of upper-bounds on epidemic trajectories allowed early predictions of mortality burden for unmitigated COVID-19 epidemics in these populations, predictions that were more accurate for counties in states without mask-wearing mandates. We discuss how this method could be used for future epidemics, including seasonal epidemics caused by influenza or ongoing epidemics caused by new SARS-CoV-2 variants.Press SummaryWhy, despite no statewide mask-wearing mandates or other restrictions like restaurant closures, did South Dakota’s COVID-19 epidemic peak not in January, when seasonal forcing wanes, but in early November? Why are we not seeing a resurgent epidemic in Florida or Texas, where non-pharmaceutical interventions have been relaxed for months? How can we compare the current outbreak in India with other countries’ epidemics to contextualize the speed of the Indian outbreak and estimate the potential loss of life?We have developed a new method of visualizing epidemics in progress that can help to compare distinct COVID-19 outbreaks to understand, in specific cases like South Dakota, why they peaked when they did. The “when” in this case does not refer to prediction of a calendar date, but rather a point in the accumulation of deaths in a given locale due to the disease in question. The method presented in this paper therefore essentially uses population-based burden of disease as a timescale for measuring epidemics. Just as the age of a car can be measured in years or miles, the age of a COVID-19 epidemic can be measured in days or deaths per-capita. Plotting growth rates of cases as a function of per-capita deaths 11 days later produces a real-time visual comparison of epidemics that are otherwise asynchronous in time.This approach permits both direct comparison across local outbreaks that may be disparate in time and/or place, as well as benchmarking of any outbreak against known exemplars of archetypal response strategies, such as New York City’s unmitigated urban outbreak in Spring 2020 and Sweden’s uncontained summer 2020 epidemic. Whether comparing the speed of resurgent outbreaks following relaxation in US states like Florida or the peak mortality burden in fall outbreaks across thousands of US counties with and without statewide mask-wearing mandates, this method offers a simple, intuitive tool for real-time monitoring and prediction capability connecting epidemic speed, burden, and management interventions. While our findings point to compelling epidemiological hypotheses for peaks in less-regulated states, future work is needed to confirm and extend our results predicting mortality burden at the peak of confirmed cases in the ongoing and evolving COVID-19 pandemic.