Tail of the distribution of fatalities in epidemics

Abstract

The size that an epidemic can reach, measured in terms of the number of fatalities, is an extremely relevant quantity. It has been recently claimed [Cirillo & Taleb, Nature Physics 2020] that the size distribution of major epidemics in human history is "extremely fat-tailed", i.e., asymptotically a power law, which has important consequences for risk management. Reanalyzing this data, we find that, although the fatality distribution may be compatible with a power-law tail, these results are not conclusive, and other distributions, not fat-tailed, could explain the data equally well. As an example, simulation of a log-normally distributed random variable provides synthetic data whose statistics are undistinguishable from the statistics of the empirical data. Theoretical reasons justifying a power-law tail as well as limitations in the current data are also discussed.

arXiv commentSubmitted. arXiv admin note: text overlap with arXiv:2007.06876

References in corpus (20)

• Power-law distributions in empirical data
• Power laws, Pareto distributions and Zipf's law
• Self-Organized Branching Processes: A Mean-Field Theory for Avalanches
• 25 Years of Self-Organized Criticality: Concepts and Controversies
• Tail Risk of Contagious Diseases
• Gibrat's law for cities: uniformly most powerful unbiased test of the Pareto against the lognormal
• Parameter estimation for power-law distributions by maximum likelihood methods
• Scale-free Networks Well Done
• Power-law size distributions in geoscience revisited
• Fitting Power-laws in empirical data with estimators that work for all exponents
• Power Law Distributions of Offspring and Generation Numbers in Branching Models of Earthquake Triggering
• Analysis of power-law exponents by maximum-likelihood maps
• Avalanche Merging and Continuous Flow in a Sandpile Model
• Scaling in the Timing of Extreme Events
• Non-characteristic Half-lives in Radioactive Decay
• Truncated lognormal distributions and scaling in the size of naturally defined population clusters
• Criticality and self-organization in branching processes: application to natural hazards
• Phase transition, scaling of moments, and order-parameter distributions in Brownian particles and branching processes with finite-size effects
• Finite-size scaling versus dual random variables and shadow moments in the size distribution of epidemics
• Scientific comment on "Tail risk of contagious diseases"

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