SL-BiLEM: Structured Learnable Behavior-in-the-Loop Epidemic Modeling for Forecasting and Policy Evaluation

Epidemic forecasting faces a fundamental challenge: human behavior dynamically responds to disease spread, creating feedback loops that induce distribution shifts at policy intervention points. This renders data-driven models unreliable under distribution shift. We propose \textbf{SL-BiLEM} (Structured Learnable Behavior-in-the-Loop Epidemic Model), leveraging physical constraints as regularization for robust extrapolation. The framework decomposes effective transmission as $β_{\text{eff}}(t,g) = β_0(g) \times m_{\text{policy}}(t) \times m_{\text{media}}(t) \times m_{\text{comp}}(t,g)$, where monotonicity, smoothness, and bounded-jump constraints on the learned compliance function maintain predictive validity under novel policy regimes. Beyond forecasting, SL-BiLEM enables counterfactual analysis for intervention decision support. We validate forecasting on three real-world datasets (cruise ship, school influenza, and school-district COVID-19 surveillance) and evaluate counterfactual recovery on synthetic benchmarks with known ground truth. SL-BiLEM demonstrates: (1) 76\% improvement over neural-mechanistic baselines, with only 53\% OOD degradation versus 1142\% for neural baselines under policy-induced shift; (2) 100\% bootstrap CI coverage across 27 synthetic counterfactual experiments; and (3) Treatment Effect Accuracy exceeding 0.85. These results establish SL-BiLEM as an interpretable tool for public health decision-makers seeking accurate prediction and principled intervention planning.