Tail of the distribution of fatalities in epidemics

The final size reached by an epidemic, measured in terms of the total number of fatalities, is an extremely relevant quantity. It has been recently claimed that the size distribution of major epidemics in human history is "strongly fat-tailed," i.e., a power law asymptotically, which has important consequences for risk management. From the point of view of statistical physics and complex-systems modeling this is not an unexpected outcome, nevertheless, strong empirical evidence is also necessary to support such a claim. Reanalyzing previous 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 available data are also discussed.