Beyond $R_0$: Heterogeneity in secondary infections and probabilistic epidemic forecasting

TL;DR

This paper emphasizes that understanding the distribution and heterogeneity of secondary infections, beyond just the basic reproductive number $R_0$, is crucial for accurate epidemic forecasting and outbreak size prediction.

Contribution

It extends classic network theory to incorporate heterogeneity in secondary infections and demonstrates its importance in epidemic modeling, especially for emerging diseases.

Findings

Heterogeneity significantly affects outbreak size predictions.

Incorporating secondary infection distribution improves forecasting accuracy.

Data on heterogeneity is critical for reliable epidemic estimates.

Abstract

The basic reproductive number -- $R_0$ -- is one of the most common and most commonly misapplied numbers in public health. Although often used to compare outbreaks and forecast pandemic risk, this single number belies the complexity that two different pathogens can exhibit, even when they have the same $R_0$. Here, we show how to predict outbreak size using estimates of the distribution of secondary infections, leveraging both its average $R_0$ and the underlying heterogeneity. To do so, we reformulate and extend a classic result from random network theory that relies on contact tracing data to simultaneously determine the first moment ($R_0$) and the higher moments (representing the heterogeneity) in the distribution of secondary infections. Further, we show the different ways in which this framework can be implemented in the data-scarce reality of emerging pathogens. Lastly, we demonstrate that without data on the heterogeneity in secondary infections for emerging infectious diseases like COVID-19, the uncertainty in outbreak size ranges dramatically. Taken together, our work highlights the critical need for contact tracing during emerging infectious disease outbreaks and the need to look beyond $R_0$ when predicting epidemic size.