Risk averse reproduction numbers improve resurgence detection

Abstract

The effective reproduction number R is a prominent statistic for inferring the transmissibility of infectious diseases and the effectiveness of interventions. R purportedly provides an easy-to-interpret threshold for deducing if an epidemic will grow (R > 1 ) or decline (R < 1 ). We posit that this interpretation can be misleading and overconfident when applied to infections aggregated from groups with heterogeneous dynamics. In these settings, R implicitly weights the dynamics of groups by their number of circulating infections. This induces losses in sensitivity to the dynamics of high-risk groups that may spur resurgences, promotes premature indications of epidemic control, and renders the R = 1 threshold uninformative. Applying E-optimal experimental design theory, we derive the risk averse reproduction number E to ameliorate these issues. Using analytic approaches, simulations, and a real-world case study, we find that E achieves more meaningful consensus of the dynamics across groups without being overconfident in its estimates. An E>1 generates timely resurgence signals (upweighting the impact of high-risk groups), while E < 1 ensures constituent sub-outbreaks are under control. We propose E as an alternative to R for informing policy and assessing transmissibility over large scales (e.g., state or nationwide), where well-mixed assumptions break down.