Conditional Inverse Learning of Time-Varying Reproduction Numbers Inference

TL;DR

This paper introduces CIRL, a flexible framework for estimating time-varying reproduction numbers from epidemic data, effectively capturing regime shifts and handling noisy, zero-inflated observations without strict parametric assumptions.

Contribution

CIRL combines epidemiological constraints with data-driven temporal modeling to improve robustness and responsiveness in estimating dynamic reproduction numbers.

Findings

Effective in detecting abrupt transmission changes

Robust to observation noise and zero-inflation

Performs well on synthetic and real epidemic data

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.