Power Laws in Superspreading Events: Evidence from Coronavirus Outbreaks and Implications for SIR Models

Abstract

While they are rare, superspreading events (SSEs), wherein a few primary cases infect an extraordinarily large number of secondary cases, are recognized as a prominent determinant of aggregate infection rates (R0). Existing stochastic SIR models incorporate SSEs by fitting distributions with thin tails, or finite variance, and therefore predicting almost deterministic epidemiological outcomes in large populations. This paper documents evidence from recent coronavirus outbreaks, including SARS, MERS, and COVID-19, that SSEs follow a power law distribution with fat tails, or infinite variance. We then extend an otherwise standard SIR model with estimated power law distributions, and show that idiosyncratic uncertainties in SSEs will lead to large aggregate uncertainties in infection dynamics, even with large populations. That is, the timing and magnitude of outbreaks will be unpredictable. While such uncertainties have social costs, we also find that they on average decrease the herd immunity thresholds and the cumulative infections because per-period infection rates have decreasing marginal effects. Our findings have implications for social distancing interventions: targeting SSEs reduce not only the average rate of infection (R0) but also its uncertainty. To understand this effect, and to improve inference of the average reproduction numbers under fat tails, estimating the tail distribution of SSEs is vital.

Quarantine fatigue thins fat-tailed coronavirus impacts in U.S. cities by making epidemics inevitable

“…Fat-tailed damages across disease outbreaks limit the ability to learn and prepare for future outbreaks, as the central limit theorem slows down and fails to hold with infinite moments. We extend recent results showing fat tails in superspreading events (Wong and Collins 2020;Fukui and Furukawa 2020) to demonstrate the emergence and persistence of fat tails in contacts across the U.S. We then demonstrate an interaction between these contact rate distributions and community-specific disease dynamics to create fat-tailed distributions of COVID-19 impacts (proxied by weekly cumulative cases and deaths) during the exact time when attempts at suppression were most intense.…”

“…While fat-tailed contact rates associated with superspreaders (Lloyd-Smith et al 2005, Galvani andMay 2005) increase transmission (Wong andCollins 2020, Fukui andFurukawa 2020) and case numbers (Anderson and May 1992), they also suggest a potential benefit: targeted policy interventions are more effective than they would be with thin-tailed contacts. If policy makers have access to the necessary information and a mandate to act decisively, they might take advantage of fat-tailed contacts to prevent inaction that normalizes case and death counts that would seem extreme early in the outbreak.…”

Power law behaviour in the saturation regime of fatality curves of the COVID-19 pandemic

“…Power-law behaviour is a distinct signature of complexity, and in such a guise they are expected to be present in epidemic dynamics as well. Evidences of complexity in the COVID-19 epidemic dynamics have indeed been observed in a number of recent works, most noticeably in the form of a power-law behaviour in the early growth regime of case and death curves [2][3][4][5][6][7] , but also in the long-time asymptotic of the probability to become infected [8][9][10] . It has also been pointed out that such complex behaviour lies outside the range of applicability of standard SIR-type models, and a number of alternative dynamics have been suggested, such as the recent proposal of a random walk on a hierarchic landscape of social clusters [11][12][13] .…”

Cascades - Mapping the multi-disciplinary landscape in a post-pandemic world

“…However, cascading effects in the case of a pandemic leave little option for circumvention. Super-spreader events, persons, or areas have to be identified and isolated and cannot be evaded [ 7 , 8 ]. Under funded public health systems and healthcare that functions with just-in-time models of efficiency have little redundancy or surge capacity for preventing or controlling a pandemic.…”