Ancestral process for infectious disease outbreaks with superspreading

TL;DR

This paper develops a new ancestral model for small infectious disease outbreaks that accounts for superspreading, enabling exact probability calculations and introducing the omega-coalescent for better outbreak analysis.

Contribution

It introduces the omega-coalescent model incorporating superspreading effects, providing exact ancestral probabilities for small outbreak samples.

Findings

Exact probabilities for shared infectors in small samples.

Incorporation of superspreading via Negative-Binomial distribution.

Comparison showing omega-coalescent's advantages over existing models.

Abstract

When an infectious disease outbreak is of a relatively small size, describing the ancestry of a sample of infected individuals is difficult because most ancestral models assume large population sizes. Given a set of infected individuals, we show that it is possible to express exactly the probability that they have the same infector, either inclusively (so that other individuals may have the same infector too) or exclusively (so that they may not). To compute these probabilities requires knowledge of the offspring distribution, which determines how many infections each infected individual causes. We consider transmission both without and with superspreading, in the form of a Poisson and a Negative-Binomial offspring distribution, respectively. We show how our results can be incorporated into a new lambda-coalescent model which allows multiple lineages to coalesce together. We call this new model the omega-coalescent, we compare it with previously proposed alternatives, and advocate its use in future studies of infectious disease outbreaks.