Estimating contagion dynamics models on networks via data assimilation

Network-based contagion models are widely used to describe the spread of epidemics, computer viruses and opinions, yet estimating their states, parameters and hyperparameters remains challenging, especially when only macro-level data are available. We therefore aimed to develop a data-assimilation framework capable of performing this estimation without requiring node-level observations. An ensemble Kalman filter-based approach was designed to assimilate macroscopic data into network-based Susceptible–Infected–Recovered models with heterogeneous parameters. The method was evaluated under three scenarios: (i) homogeneous parameters with known network topology; (ii) heterogeneous parameters with known topology; and (iii) homogeneous parameters with unknown topology. Across all tested scenarios, the proposed algorithms accurately estimated both the system states and the underlying parameter/hyperparameter when the network size are sufficiently large, demonstrating scalability and robustness even when only aggregate statistics were available. The results indicate that the proposed assimilation framework can reliably estimate network-based contagion dynamics from macro-level observations, obviating the need for costly node-level monitoring and offering a practical tool for real-time epidemic analysis and forecasting.