Reconciling early-outbreak estimates of the basic reproductive number and its uncertainty: framework and applications to the novel coronavirus (SARS-CoV-2) outbreak

Park, Sang Woo; Bolker, Benjamin M.; Champredon, David; Earn, David J.D.; Li, Michael; Weitz, Joshua S.; Grenfell, Bryan T.; Dushoff, Jonathan

A novel coronavirus (SARS-CoV-2) has recently emerged as a global threat. As the epidemic progresses, many disease modelers have focused on estimating the basic reproductive number Ro -- the average number of secondary cases caused by a primary case in an otherwise susceptible population. The modeling approaches and resulting estimates of Ro vary widely, despite relying on similar data sources. Here, we present a novel statistical framework for comparing and combining different estimates of Ro across a wide range of models by decomposing the basic reproductive number into three key quantities: the exponential growth rate $r$, the mean generation interval $\bar G$, and the generation-interval dispersion $\kappa$. We then apply our framework to early estimates of Ro for the SARS-CoV-2 outbreak. We show that many early Ro estimates are overly confident. Our results emphasize the importance of propagating uncertainties in all components of Ro, including the shape of the generation-interval distribution, in efforts to estimate Ro at the outset of an epidemic.