The basic reproductive number --- R_0 --- is one of the most common and most commonly misapplied numbers in public health. Nevertheless, estimating R_0 for every transmissible pathogen, emerging or endemic, remains a priority for epidemiologists the world over. 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. Further, we show how this framework is robust in the face of the typically limited amount of data for emerging pathogens. Lastly, we demonstrate that without data on the heterogeneity in secondary infections for emerging pathogens like 2019-nCoV , the uncertainty in outbreak size ranges dramatically , in the case of 2019-nCoV from 5-40%DIFDELCMD < \\%%% %DIF < of susceptible individuals. 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.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 %DIFDELCMD < \\%%% %DIF < of susceptible individuals. 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.abstract . 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.
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Nevertheless, estimating R_0 for every transmissible pathogen, emerging or endemic, remains a priority for epidemiologists the world over.
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predicting outbreak size requires both an estimate of
to predict outbreak size using estimates of the distribution of secondary infections, leveraging both its average
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an estimate of the heterogeneity in the number of secondary infections. To facilitate rapid determination of outbreak risk, we propose a reformulation of a
the underlying heterogeneity. To do so, we reformulate and extend a
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how this framework is robust in the face of the typically limited amount of data for
the different ways in which this framework can be implemented in the data-scarce reality of
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pathogens like 2019-nCoV
infectious diseases like COVID-19
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, in the case of 2019-nCoV from 5-40
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. 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.