Fast, Frequentist Estimation of Epidemic Reproduction Numbers

The effective reproduction number $R_t$ is one of the most important indicators of epidemic dynamics. Estimating $R_t$, typically from case reports or hospitalization counts, poses a challenging inverse problem. One key issue is lag: $R_t$ acts at the moment of transmission, while the data it generates surface days later. To handle this delay and infer recent infections in real time, popular methods take a Bayesian approach, which can be slow and sensitive to prior specification. As an alternative, we propose ConvRt, a frequentist method for retrospective and real-time estimation. ConvRt deconvolves latent infections and then estimates $R_t$ with successive penalized-likelihood steps, using a spline basis to model smooth curves. Across both stylized and data-driven simulations, we demonstrate favorable performance in point estimation, uncertainty quantification, and runtime. Moreover, by untangling smoothness from future projections, ConvRt enables researchers to assess which qualitative narratives about $R_t$ the data support.