On the emergence of a power law in the distribution of COVID-19 cases

Beare, Brendan K.; Toda, Alexis Akira

doi:10.1016/j.physd.2020.132649

Cited by 51 publications

(67 citation statements)

References 62 publications

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“…First, we may be concerned that, even if Φ is a power law distribution, F may not be a power law distribution. A counterexample is that a geometric Brownian motion with stochastic stopping time that follows exponential distribution can also generate power law distributions of the tail (Beare and Toda, 2020). That is, the tail property of Φ needs not be due to tails of F: for ∑ t z it , it could also due to some individuals staying infectious for an extremely long periods.…”

Section: Appendix a Empirical Appendixmentioning

confidence: 99%

“…We emphasize another dimension of targeting: targeting toward large social gatherings, and this policy reduces the uncertainty regarding various epidemiological outcomes. Another related paper is Beare and Toda (2020). They document that the cumulative number of infected population across cities and countries is closely approximated by a power law distribution.…”

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confidence: 99%

“…These include the city size (Zipf, 1949), the firm size (Axtell, 2001), income (Atkinson et al, 2011), wealth (Kleiber and Kotz, 2003), consumption (Toda and Walsh, 2015) and even the size of the earthquakes (Gutenberg and Richter, 1954), the moon craters and solar flares (Newman, 2005). Regarding COVID-19, Beare and Toda (2020) document that the cumulative number of infected population across cities and countries is closely approximated by a power law distribution. They then argue that the standard SIR model is able to explain the fact.…”

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confidence: 99%

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

Fukui

Furukawa

2020

Preprint

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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.

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Section: Appendix a Empirical Appendixmentioning

confidence: 99%

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confidence: 99%

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confidence: 99%

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

Fukui

Furukawa

2020

Preprint

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“…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] .…”

Section: Introductionmentioning

confidence: 93%

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

Vasconcelos

Macêdo

Duarte-Filho

et al. 2020

Preprint

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We apply a versatile growth model, whose rate of change is given by a generalised beta distribution, to describe the complex behaviour of the fatality curves of the COVID-19 disease for several countries in Europe and Asia. We show that the COVID-19 epidemic curves not only may present a subexponential early growth but can also exhibit a similar subexponential (power-law) behaviour in the saturation regime. We argue that the power-law exponent of the latter regime, which measures how quickly the curve approaches the plateau, is directly related to control measures, in the sense that the less strict the control, the smaller the exponent and hence the slower the diseases progresses to its end. The power-law saturation uncovered here is an important result, because it signals to health authorities that it is important to keep control measures for as long as possible, so as to avoid a slow, power-law ending of the disease. The slower the approach to the plateau, the longer the virus lingers on in the population, and the greater not only the death toll but also the risk of resurgence.

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“…Within the nonlinear dynamics community, a majority of papers on COVID-19 have used new and traditional techniques to analyze and predict the spread of cases and deaths [21] , [22] , [23] , [24] . Of these, improvements to SIR models [25] , [26] , [27] , [28] , [29] , [30] , [31] and power-law models [32] , [33] , [34] , [35] have been the most popular. There is an absence of research that studies financial markets in conjunction with the spread of the virus.…”

Section: Introductionmentioning

confidence: 99%

Association between COVID-19 cases and international equity indices

James

Menzies

2021

Physica D: Nonlinear Phenomena

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This paper analyzes the impact of COVID-19 on the populations and equity markets of 92 countries. We compare country-by-country equity market dynamics to cumulative COVID-19 case and death counts and new case trajectories. First, we examine the multivariate time series of cumulative cases and deaths, particularly regarding their changing structure over time. We reveal similarities between the case and death time series, and key dates that the structure of the time series changed. Next, we classify new case time series, demonstrate five characteristic classes of trajectories, and quantify discrepancy between them with respect to the behavior of waves of the disease. Finally, we show there is no relationship between countries’ equity market performance and their success in managing COVID-19. Each country’s equity index has been unresponsive to the domestic or global state of the pandemic. Instead, these indices have been highly uniform, with most movement in March.

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On the emergence of a power law in the distribution of COVID-19 cases

Cited by 51 publications

References 62 publications

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

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

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

Association between COVID-19 cases and international equity indices

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