Encoding generation time changes within reproduction numbers

Abstract

AbstractWe introduce theangular reproduction numberΩ, 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 either inferRor 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 variants A and B). We find that Ω responds meaningfully to mismatches inwwhile maintaining most of the interpretability ofR. Additionally, we prove that Ω>1 impliesR>1 and that Ω agrees withron the relative transmissibility of pathogens. Estimating Ω is no harder than inferringR, uses existing software, and requires no generation time measurement. These advantages come at the expense of selecting one free parameter. We propose Ω as a useful statistic for tracking and comparing infectious disease dynamics that may better reflect the impact of interventions when those interventions concurrently change bothRandwor alter the relative risk of co-circulating pathogens.