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

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 ℛ ₀ – the average number of secondary cases caused by a primary case in an otherwise susceptible population. The modeling approaches and resulting estimates of ℛ ₀ vary widely, despite relying on similar data sources. Here, we present a novel statistical framework for comparing and combining different estimates of ℛ ₀ 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 <inline-formula> <alternatives> <inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="20019877v4_inline1.gif"/> </alternatives> </inline-formula> , and the generation-interval dispersion κ . We then apply our framework to early estimates of ℛ ₀ for the SARS-CoV-2 outbreak. We show that many early ℛ ₀ estimates are overly confident. Our results emphasize the importance of propagating uncertainties in all components of ℛ ₀ , including the shape of the generation-interval distribution, in efforts to estimate ℛ ₀ at the outset of an epidemic.