Before revision:  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 predicting outbreak size requires both an estimate of R_0 and an estimate of the heterogeneity in the number of secondary infections. To facilitate rapid determination of outbreak risk, we propose a reformulation of 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.
After revision:  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 predicting outbreak size requires both an estimate of 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.