Conditional Inverse Learning of Time-Varying Reproduction Numbers Inference

2026-03-18

AI Summary

Estimating the time-varying effective reproduction number from epidemic incidence data constitutes an ill-posed inverse problem; conventional approaches, relying on strong structural assumptions, struggle to adapt to non-stationary transmission dynamics, resulting in delayed responses and reduced accuracy. This work proposes a Conditional Inverse Reproduction Number Learning (CIRL) framework that learns a conditional mapping from historical incidence patterns and temporal information to the reproduction number, using the renewal equation as a forward operator. By softly integrating epidemiological constraints with explicit temporal encoding, CIRL avoids rigid parametric assumptions while preserving epidemiological consistency, thereby significantly enhancing robustness and sensitivity to abrupt transmission shifts and zero-inflated observations. Experiments on both synthetic and real-world SARS and COVID-19 datasets demonstrate its superior noise resilience and rapid responsiveness.

Technology Category

• Machine Learning: Imitation Learning & Inverse Reinforcement Learning
• Reasoning under Uncertainty: Relational Probabilistic Models
• Constraint Satisfaction and Optimization: Constraint Learning and Acquisition

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Responsible Web: Measurement, analysis, and circumvention of Web censorship

Abstract

Estimating time-varying reproduction numbers from epidemic incidence data is a central task in infectious disease surveillance, yet it poses an inherently ill-posed inverse problem. Existing approaches often rely on strong structural assumptions derived from epidemiological models, which can limit their ability to adapt to non-stationary transmission dynamics induced by interventions or behavioral changes, leading to delayed detection of regime shifts and degraded estimation accuracy. In this work, we propose a Conditional Inverse Reproduction Learning framework (CIRL) that addresses the inverse problem by learning a {conditional mapping} from historical incidence patterns and explicit time information to latent reproduction numbers. Rather than imposing strongly enforced parametric constraints, CIRL softly integrates epidemiological structure with flexible likelihood-based statistical modeling, using the renewal equation as a forward operator to enforce dynamical consistency. The resulting framework combines epidemiologically grounded constraints with data-driven temporal representations, producing reproduction number estimates that are robust to observation noise while remaining responsive to abrupt transmission changes and zero-inflated incidence observations. Experiments on synthetic epidemics with controlled regime changes and real-world SARS and COVID-19 data demonstrate the effectiveness of the proposed approach.

Problem

• time-varying reproduction number
• inverse problem
• epidemic incidence
• non-stationary transmission dynamics
• regime shifts

Innovation

• conditional inverse learning
• time-varying reproduction number
• renewal equation
• epidemiological modeling
• non-stationary dynamics