Assessing epidemic curves for evidence of superspreading

TL;DR

This paper introduces a Bayesian model for epidemic curves that explicitly accounts for heterogeneity in individual infectiousness, revealing significant superspreading effects in COVID-19 data and impacting estimates of the reproduction number.

Contribution

It presents a new discrete-time branching process model incorporating heterogeneity, improving understanding of superspreading and its influence on epidemic dynamics.

Findings

Heterogeneity leads to less certainty in $R_t$ estimates.

20% most infectious cases cause 75-98% of secondary infections.

Heterogeneity significantly affects epidemic parameter estimation.

Abstract

The expected number of secondary infections arising from each index case, referred to as the reproduction or $R$ number, is a vital summary statistic for understanding and managing epidemic diseases. There are many methods for estimating $R$; however, few explicitly model heterogeneous disease reproduction, which gives rise to superspreading within the population. We propose a parsimonious discrete-time branching process model for epidemic curves that incorporates heterogeneous individual reproduction numbers. Our Bayesian approach to inference illustrates that this heterogeneity results in less certainty on estimates of the time-varying cohort reproduction number $R_t$. We apply these methods to a COVID-19 epidemic curve for the Republic of Ireland and find support for heterogeneous disease reproduction. Our analysis allows us to estimate the expected proportion of secondary infections attributable to the most infectious proportion of the population. For example, we estimate that the 20% most infectious index cases account for approximately 75-98% of the expected secondary infections with 95% posterior probability. In addition, we highlight that heterogeneity is a vital consideration when estimating $R_t$.