Tail of the distribution of fatalities in epidemics

TL;DR

This paper investigates the distribution of epidemic fatalities, questioning the claim that it is extremely fat-tailed, and finds that alternative distributions can fit the data equally well, highlighting uncertainties in risk assessment.

Contribution

It critically reanalyzes epidemic fatality data, showing that fat-tailed distributions are not conclusively supported and exploring alternative models like log-normal distributions.

Findings

Fatality distribution may be compatible with power-law tails.

Alternative distributions, such as log-normal, fit the data well.

Current data limitations hinder definitive conclusions.

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.