When is the R = 1 epidemic threshold meaningful?

The effective reproduction number R is a predominant statistic for tracking the transmissibility of infectious diseases and informing public health policies. An estimated R=1 is universally interpreted as indicating epidemic stability and is a critical threshold for deciding whether infections will grow (R>1) or fall (R<1). We demonstrate that this threshold, which is typically computed over coarse spatial scales, seldom signifies stability because those scales frequently average stochastic infections from groups with heterogeneous transmission characteristics. Groups with falling and rising infections counteract and early-warning signals from resurging groups are obscured by noisy fluctuations from stable groups with larger infections. We prove that an estimated R=1 is consistent with a vast space of epidemiologically diverse scenarios, often leading to false-positive stability signals that diminish its predictive and policymaking value. In contrast, we show that a popular, alternative definition of transmissibility, relating to the next-generation matrix of the groups, overcorrects for this issue and yields false-negative stability signals by maximising sensitivity to stochasticity. We find a recently developed statistic, E, derived from R using experimental design theory, rigorously constrains the space of scenarios corresponding to stability, while limiting noise sensitivity. We establish that E=1 is a more practical and meaningful stability threshold.