Fast, Frequentist Estimation of Epidemic Reproduction Numbers

2026-07-07

AI Summary

Accurate real-time estimation of the effective reproduction number $R_t$ is hindered by reporting delays and the computational inefficiency and prior sensitivity of conventional Bayesian approaches. This work proposes ConvRt, a fast frequentist method that decouples smooth inference of $R_t$ from future forecasting by deconvolving the latent infection process and employing spline basis functions with penalized likelihood for smooth modeling. By avoiding reliance on Bayesian priors, ConvRt directly infers the dynamic trajectory of $R_t$ from observed data. Evaluations on both simulated and real-world epidemic data demonstrate that ConvRt achieves higher point estimation accuracy, provides reliable uncertainty quantification, and offers substantially improved computational speed compared to existing methods.

Abstract

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.

Problem

• effective reproduction number
• epidemic dynamics
• reporting delay
• real-time estimation
• inverse problem

Innovation

• ConvRt
• effective reproduction number
• deconvolution
• penalized likelihood
• spline basis