Pair-based estimators of infection and removal rates for stochastic epidemic models

2026-03-23

AI Summary

This study addresses the challenge in infectious disease surveillance where only removal times are observed while infection times are missing, leading to substantial bias and instability in existing estimation methods under moderate to high basic reproduction numbers (R₀). To tackle this issue within partially observed stochastic SIR/SEIR models, the authors propose a novel strategy that leverages a small number of fully observed infection cycles to calibrate an imputation estimator based on pairwise exposure terms, coupled with a studentized parametric bootstrap for bias correction and uncertainty quantification. The method achieves markedly improved accuracy in estimating transmission rates with as few as several dozen complete infection cycles, thereby overcoming the reliance of conventional approaches on fully observed data. A closed-form expression for the pairwise exposure term is derived theoretically. Simulations demonstrate superior stability at moderate-to-high R₀, and the approach successfully reproduces the between-class transmission heterogeneity observed in the 1861 Hagelloch measles outbreak.

Technology Category

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

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

Stochastic epidemic models can estimate infection and removal rates, and derived quantities such as the basic reproductive number ($R_0$), when both infection and removal times are observed. In practice, however, removal times are often available while infection times are not, and existing methods that rely only on removal times can become unstable or biased. We study inference for stochastic SIR/SEIR models in a partial--observation setting. We develop imputation--based estimators that use a small calibration sample of fully observed infectious periods, derive closed--form expressions for the pairwise exposure terms they require, and use a studentized parametric bootstrap for bias correction and uncertainty quantification. In simulations, removal time--only methods performed poorly in moderate to large $R_0$ scenarios, while observing even tens of complete infectious periods substantially improved the estimation of the infection rate. A reanalysis of the 1861 Hagelloch measles outbreak under simulated missingness recovered stable qualitative differences in transmission between school classes. Based on our results, we advocate for the targeted collection of a modest number of complete infectious periods as a means of improving surveillance in the early stages of an epidemic.

Problem

• stochastic epidemic models
• infection rate estimation
• partial observation
• removal times
• missing infection times

Innovation

• pair-based estimator
• imputation-based inference
• stochastic epidemic model
• infectious period calibration
• studentized parametric bootstrap