Conditional Inverse Learning of Time-Varying Reproduction Numbers Inference

• URL: http://arxiv.org/abs/2603.17549v1
• Date: Wed, 18 Mar 2026 09:52:41 GMT
• Title: Conditional Inverse Learning of Time-Varying Reproduction Numbers Inference
• Abstract summary: Estimating time-varying reproduction numbers from epidemic incidence data is a central task in infectious disease surveillance.<n>We propose a Conditional Inverse Reproduction Learning framework (CIRL) that addresses the inverse problem by learning a conditional mapping from historical incidence patterns to latent reproduction numbers.<n>The resulting framework combines epidemiologically grounded constraints with data-driven temporal representations, producing reproduction number estimates that are robust to observation noise.
• Score: 0.7367227178198079
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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