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

ABSTRACT

We introduce the angular reproduction number Ω, 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 infer either 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 Ω responds meaningfully to mismatches and time-variations in w while mostly maintaining the interpretability of R. We prove that Ω > 1 implies R > 1 and that Ω agrees with r on the relative transmissibility of pathogens. Estimating Ω 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 Ω 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.