Angular reproduction numbers improve estimates of transmissibility when disease generation times are misspecified or time-varying

Abstract

We introduce theangular reproduction number Ω, which measures time-varying changes in epidemic transmissibility resulting from variations in both the effective reproduction numberR, and generation time distributionw. Predominant approaches for tracking pathogen spread infer eitherRor the epidemic growth rater. However,Ris biased by mismatches between the assumed and truew, whileris difficult to interpret in terms of the individual-level branching process underpinning transmission.Randrmay also disagree on the relative transmissibility of epidemics or variants (i.e.rA>rBdoes not implyRA>RBfor variantsAandB). We find thatΩresponds meaningfully to mismatches and time-variations inwwhile mostly maintaining the interpretability ofR. We prove thatΩ> 1 impliesR> 1 and thatΩagrees withron the relative transmissibility of pathogens. EstimatingΩis no more difficult than inferringR, uses existing software, and requires no generation time measurements. These advantages come at the expense of selecting one free parameter. We proposeΩas complementary statistic toRandrthat improves transmissibility estimates whenwis misspecified or time-varying and better reflects the impact of interventions, when those interventions concurrently changeRandwor alter the relative risk of co-circulating pathogens.