Superspreaders and High Variance Infectious Diseases

TL;DR

This paper analyzes how high transmission variability, especially superspreaders, affects outbreak probabilities in pandemics like COVID-19, using stochastic models to derive analytical formulas and explore implications.

Contribution

It introduces an approximate analytical formula for outbreak probability in high variance infection regimes within stochastic branching processes, validated numerically.

Findings

High variance can prevent outbreaks even when R0 > 1.

Superspreaders significantly influence outbreak dynamics.

The formula's validity varies across different scenarios.

Abstract

A well-known characteristic of pandemics such as COVID-19 is the high level of transmission 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 this phenomenon requires the analysis of the effect of the variance and higher moments of the infection distribution. Working in the framework of stochastic branching processes, we derive an approximate analytical formula for the probability of an outbreak in the high variance regime of the infection distribution, verify it numerically and analyze its regime of validity in various examples. We show that it is possible for an outbreak not to occur in the high variance regime even when the basic reproduction number $R_0$ is larger than one and discuss the implications of our results for COVID-19 and other pandemics.