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.