On the Connection Between Differential Population Growth Rate and Epidemic Reproduction Numbers

Abstract

During pandemics, public health agencies need to rapidly assess whether a new viral variant is more transmissible than existing lineages. For co-circulating variants, relative fitness can be expressed as a selective coefficient, as the differential population growth rate (DPGR) estimated from genomic surveillance, or, with additional assumptions, as a contrast in epidemic reproduction numbers $R_t$. We show that DPGR estimates a pairwise growth-rate difference. Under a specified generation-interval model, this difference can be transformed into reproduction-number space; in the equal-generation-time SIR special case, it reduces to a scaled difference in variant-specific $R_t$. Related growth-rate contrasts also appear in multinomial logistic and growth-advantage random-walk models, although those methods differ from DPGR in likelihood, smoothing, priors, and data inputs. We evaluate the theory across five SARS-CoV-2 and influenza analyses totaling more than 2,200 matched data points. SIR simulation recovers the expected mapping when the true $R_t$ is known, and retrospective SARS-CoV-2 analyses show sustained DPGR signals 43 to 65 days before variant dominance, with 95\% sign accuracy in our analysis. DPGR is approximately transitive across lineage triplets, near zero for selected functionally similar sublineages, and directionally consistent across countries. These results connect sequence-count-based fitness estimates to reproduction-number contrasts through an assumption-explicit growth-rate bridge.