Equation Learning for Agent-Based Infectious Disease Models

  • Catlin, Jonah (North Carolina State University)
  • Özaltin, Osman (North Carolina State University)
  • Mayorga, Maria (North Carolina State University)
  • Swann, Julie (North Carolina State University)
  • Sheeran, Paschal (The University of North Carolina at Chapel Hi)
  • Flores, Kevin (North Carolina State University)

Please login to view abstract download link

Agent-based models (ABMs) are widely used to study infectious disease dynamics to capture heterogeneous contacts, stochastic transmission, and complex intervention strategies. However, their computational cost limits high dimensional parameter estimation, uncertainty quantification, and real-time policy decision making [1]. In contrast, compartmental ordinary differential equation (ODE) models are computationally efficient and analytically tractable, but often rely on simplifying assumptions that fail to capture heterogeneities modeled by ABMs. We develop an equation-learning framework that bridges these modeling paradigms by learning an interpretable ODE surrogate directly from stochastic ABM simulations. Using the COVID-19 agent-based model Covasim, we construct a 12-compartment ODE system incorporating testing and contact tracing, and treat key epidemiological rates such as effective contact and tracing rates as state-dependent functions rather than constants. These functions are inferred from ABM-generated data using Biologically Informed Neural Networks (BINNs) [2], which simultaneously denoise state trajectories and enforce epidemiological constraints. To recover interpretability and enable downstream analysis, we apply sparse regression to extract symbolic representations of the learned parameter functions. The resulting ODE surrogates accurately reproduce ABM trajectories under both constant and time-varying contact tracing interventions, outperforming constant-parameter ODE benchmarks in normalized root mean square error across disease compartments. To quantify the impact of ABM stochasticity, we integrate Approximate Bayesian Computation (ABC) to infer posterior distributions over the symbolic coefficients, yielding posterior predictive intervals that capture variability across independent ABM realizations. This work provides a practical, uncertainty-aware methodology for coarse-graining complex agent-based infectious disease models into fast, interpretable ODE systems. The proposed framework enables efficient simulation, reproduction number analysis, and comparative evaluation of intervention strategies, and is broadly applicable to agent-based models in epidemiology and other applied dynamical systems.