Superspreaders and high variance infectious diseases

A well-known characteristic of recent pandemics is the high level of heterogeneity in the infection spread: not all infected individuals spread the disease at the same rate and some individuals (superspreaders) are responsible for most of the infections. To quantify the effects of this phenomenon, we analyze the effect of the variance and higher moments of the infection distribution on the spread of the disease. Working in the framework of stochastic branching processes, we derive an approximate analytical formula for the probability of avoiding an outbreak in the high variance regime of the infection distribution, verify it numerically and analyze its regime of validity in various examples. We perform population based simulations and show that, as predicted by the mathematical model, it is possible for an outbreak not to occur in the high variance regime even when the basic reproduction number R0 is larger than 1. The applicability of our results to the current COVID-19 is restricted to scenarios where imposed measures are able to reduce significantly the number of infected individuals and the high basic reproduction number. We note that our analysis may find implications in general information spread scenarios.