A State-Space Agent-Based Model for Infectious Disease Spread

We present a novel framework for epidemiological disease spread modeling that combines agent-based simulation with Boolean state-space representations and optimal filtering for state estimation under noisy observations. Our approach models individual agents in discrete Susceptible-Exposed-Infected-Recovered (SEIR) states using a compact 2-bit Boolean representation, with agent interactions governed by scheduled contact patterns. To address the challenge of inferring latent infection states from limited and noisy testing data, we develop two complementary inference approaches: (1) a Boolean Kalman particle filter for small populations that tracks the full joint distribution over agent states, and (2) a mean-field approximation for large populations that factorizes the posterior into independent marginal distributions, enabling scalability to realistic population sizes. Unlike continuous-state Kalman filters, our methods naturally handle the discrete nature of epidemiological states while accommodating realistic observation models where only a subset of agents are tested at each time step, with test results subject to false positive and false negative errors. We demonstrate that this framework enables accurate reconstruction of population-level infection dynamics and individual agent states from sparse, noisy observations across populations from 100 to 50,000 agents, providing a computationally tractable approach for real-time epidemic monitoring.