The role of super-spreaders in modeling of SARS-CoV-2

TL;DR

This paper investigates the impact of super-spreaders on SARS-CoV-2 transmission modeling in finite populations, demonstrating that stochastic infectivity variations influence outbreak probability but not outbreak shape, with new convergence results for models.

Contribution

It extends existing stochastic models to finite populations with realistic offspring distributions, including fat-tailed ones for super-spreaders, and provides new theoretical convergence results.

Findings

Super-spreaders significantly affect outbreak probability.

Deterministic outbreak curves are unaffected by infectivity variations.

New convergence theorems for stochastic models with finite variance offspring distributions.

Abstract

In stochastic modeling of infectious diseases, it has been established that variations in infectivity affect the probability of a major outbreak, but not the shape of the curves during a major outbreak, which is predicted by deterministic models [Diekmann et al., 2012]. However, such conclusions are derived under idealized assumptions such as the population size tending to infinity, and the individual degree of infectivity only depending on variations in the infectiousness period. In this paper we show that the same conclusions hold true in a finite population representing a medium size city, where the degree of infectivity is determined by the offspring distribution, which we try to make as realistic as possible for SARS-CoV-2. In particular, we consider distributions with fat tails, to incorporate the existence of super-spreaders. We also provide new theoretical results on convergence of stochastic models which allows to incorporate any offspring distribution with a finite variance.