Disease Momentum: Estimating the Reproduction Number in the Presence of Superspreading

TL;DR

This paper investigates how superspreading affects the estimation of the reproduction number in infectious diseases, demonstrating increased uncertainty and providing a formula linking superspreading to credible interval width, with a case study on COVID-19 in Austria.

Contribution

It introduces an extension to existing models to account for superspreading, improving the understanding of uncertainty in reproduction number estimates.

Findings

Superspreading increases estimation uncertainty.

Prediction intervals are more accurate with superspreading.

Derived a formula linking superspreading to credible interval width.

Abstract

A primary quantity of interest in the study of infectious diseases is the average number of new infections that an infected person produces. This so-called reproduction number has significant implications for the disease progression. There has been increasing literature suggesting that superspreading, the significant variability in number of new infections caused by individuals, plays an important role in the spread of SARS-CoV-2. In this paper, we consider the effect that such superspreading has on the estimation of the reproduction number and subsequent estimates of future cases. Accordingly, we employ a simple extension to models currently used in the literature to estimate the reproduction number and present a case-study of the progression of COVID-19 in Austria. Our models demonstrate that the estimation uncertainty of the reproduction number increases with superspreading and that this improves the performance of prediction intervals. Of independent interest is the derivation of a transparent formula that connects the extent of superspreading to the width of credible intervals for the reproduction number. This serves as a valuable heuristic for understanding the uncertainty surrounding diseases with superspreading.