Simultaneous estimation of the effective reproduction number and the time series of daily infections: Application to Covid-19

2025-06-26

AI Summary

Estimating the time-varying effective reproduction number ((R_t)) and daily incident infections simultaneously and robustly remains challenging for infectious disease surveillance—especially during early and late epidemic phases, where cumulative errors from conventional three-step approaches degrade stability and accuracy. To address this, we propose a Bayesian joint inference framework based on a self-exciting point process model. Our method employs Markov Chain Monte Carlo (MCMC) to directly sample the joint posterior distribution of (R_t) and the latent incident infection counts, thereby avoiding error propagation inherent in sequential estimation. Evaluations on real Swiss COVID-19 data and multiple synthetic datasets demonstrate substantial improvements in estimation accuracy for both (R_t) and infection trajectories—particularly under sparse-data conditions at epidemic onset and decline. Moreover, the approach delivers full uncertainty quantification, enhancing the scientific rigor and interpretability of public health decision-making.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Intelligent Robots: State Estimation
• Machine Learning: Calibration & Uncertainty Quantification

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Security and Privacy: Large-scale security measurements
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics

Abstract

The time varying effective reproduction number is an important parameter for communication and policy decisions during an epidemic. It is difficult to estimate because it depends on latent variables such as new infections and other characteristics of an epidemic which have to be inferred from available data. In this paper, we present new statistical methods for a popular model which defines the effective reproduction number based on self-exciting dynamics of new infections. Such a model is conceptually simple and less susceptible to misspecifications than more complicated multi-compartment models. In contrast to the state-of-the-art three-step estimation procedure of citet{huisman2022estimation}, we present a coherent Bayesian method that approximates the joint posterior of daily new infections and reproduction numbers given the data using a novel Markov chain Monte Carlo (MCMC) algorithm. Comparing our method with that of citet{huisman2022estimation}, both with daily confirmed cases from Switzerland in the Covid-19 epidemic and with simulated data, we find that our method is more accurate, especially near the beginning and end of the observation period.

Problem

• Estimating time-varying effective reproduction number for epidemics
• Inferring daily new infections from available epidemic data
• Improving accuracy of Bayesian estimation for epidemic parameters

Innovation

• Bayesian method for joint posterior estimation
• Novel MCMC algorithm for inference
• Self-exciting dynamics model simplification