Encoding generation time changes within reproduction numbers

We introduce the angular reproduction number {Omega}, which measures time-varying changes in epidemic transmissibility resulting from variations in both the effective reproduction number R, and generation time distribution w. Predominant approaches for tracking pathogen spread either infer R or the epidemic growth rate r. However, R is biased by mismatches between the assumed and true w, while r is difficult to interpret in terms of the individual-level branching process underpinning transmission. R and r may also disagree on the relative transmissibility of epidemics or variants (i.e., rA>rB does not imply RA>RB for variants A and B). We find that {Omega} responds meaningfully to mismatches and time-variations in w while mostly maintaining the interpretability of R. We prove that {Omega}>1 implies R>1 and that {Omega} agrees with r on the relative transmissibility of pathogens. Estimating {Omega} is no more difficult than inferring R, uses existing software, and requires no generation time measurements. These advantages come at the expense of selecting one free parameter. We propose {Omega} as complementary statistic to R and r that improves transmissibility estimates when w is misspecified or time-varying and better reflects the impact of interventions, when those interventions concurrently change R and w or alter the relative risk of co-circulating pathogens.