Graph World Models for Constrained Epidemic Policy Planning

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.

World models are increasingly used for planning, yet most analyses of rollout error assume vector-valued states and scalar error amplification. Many planning environments, however, are naturally graph-structured: agents, tools, skills, routes, and dependencies interact through evolving relations. In this work, we study how prediction errors accumulate in Graph World Models (GWMs). We formulate fixed-edge and dynamic-edge GWM rollouts under a unified state-action transition framework and derive topology-aware error bounds. For fixed-edge rollouts, we show that long-horizon node error separates into a topology factor, governed by the graph spectral radius, and a model factor, governed by layer spectral norms. For dynamic-edge rollouts, we introduce a joint node-edge error operator that captures feedback between feature prediction and structure prediction, revealing when edge errors amplify future message passing. Motivated by these bounds, we propose Error-Aware GWM, a training objective that combines spectral regularization, rollout consistency, and critical-node weighting. Across synthetic graph topologies and heterogeneous agent-graph testbeds, we find that rollout error and planning regret grow with horizon, that dynamic-edge training is necessary when structure evolves, and that Error-Aware GWM improves long-horizon stability without sacrificing one-step accuracy. Our results characterize when graph world models remain reliable under autoregressive planning and when topology makes them fail.

Graph-based world models have recently emerged as a means of learning transitions over relational state representations. However, existing approaches are largely limited to fixed-topology graphs or deterministic, fully observable environments. We propose the Graph Dynamics Model (GDM), a world model for graph-structured observations that is designed to handle the more general setting of evolving topologies in stochastic and partially observable environments. The GDM uses a sparse recurrent adjacency matrix to model topology updates and perform message passing, together with a recurrent state-space architecture for modelling stochastic transitions. Furthermore, we identify a gap in the evaluation of graph-based world models, as existing methods do not provide a means of comparing predicted and true distributions over the joint graph state comprising the interdependent topology, node features, and graph features. We therefore introduce the Graph Distribution Distance (GDD) metric, which uses maximum mean discrepancy with a graph kernel to comprehensively compare joint next-state distributions. We evaluate the GDM across several environments, including stochastic and partially observable settings. We demonstrate that GDM outperforms baseline models and displays zero-shot generalisation on large graphs.