Beyond R(0): heterogeneity in secondary infections and probabilistic epidemic forecasting

Hébert-Dufresne, Laurent; Althouse, Benjamin M.; Scarpino, Samuel V.; Allard, Antoine

The basic reproductive number, R(0), is one of the most common and most commonly misapplied numbers in public health. Often used to compare outbreaks and forecast pandemic risk, this single number belies the complexity that different epidemics can exhibit, even when they have the same R(0). Here, we reformulate and extend a classic result from random network theory to forecast the size of an epidemic using estimates of the distribution of secondary infections, leveraging both its average R(0) and the underlying heterogeneity. Importantly, epidemics with lower R(0) can be larger if they spread more homogeneously (and are therefore more robust to stochastic fluctuations). We illustrate the potential of this approach using different real epidemics with known estimates for R(0), heterogeneity and epidemic size in the absence of significant intervention. Further, we discuss 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).