Tail risk of contagious diseases

Sreekar Vadlamani, TIFR-CAM

In a pandemic situation, governments are often faced with the unenviable task of taking tough decisions that have far-reaching consequences. It is thus critical that a thorough risk analysis is carried out, which requires that the pandemic be quantified by using estimates/statistics. One commonly used quantification of the pandemic is the number of fatalities caused by the pandemic, and often data from past pandemics can be used to estimate the worst-case scenario. It is here that the authors in this paper caution against using estimates of the fatalities based on the bulk of the distribution (mean, variance, etc.), and instead argue that estimates based on the tail of the distribution, like mean excess function, are more relevant
 

Left: The bulk and the tail portions of a probability density. Right: Contrasting the light and heavy-tailed probability distributions.
 

Specifically, the authors analyzed data from the past 2500 years, and concluded that the probability distribution of fatalities in pandemics exhibits a ‘heavy-tailed behavior’. Meaning, pandemics can cause a very large number of fatalities with significantly high probability. Additionally, the authors indicate that the distribution of fatalities is so ‘heavy-tailed’ that the mean of the distribution does not exist (it is infinite!), further corroborating the usage of estimates based on the tail of the distribution.
 

[Last update 02 Jul 2020]