Efficient sequential Bayesian inference for state-space epidemic models using ensemble data assimilation

Estimating latent epidemic states and model parameters from partially observed, noisy data remains a major challenge in infectious disease modeling. State-space formulations provide a coherent probabilistic framework for such inference, yet fully Bayesian estimation is often computationally prohibitive because evaluating the observed-data likelihood requires integration over a latent trajectory. The Sequential Monte Carlo squared (SMC2) algorithm offers a principled approach for joint state and parameter inference, combining an outer SMC sampler over parameters with an inner particle filter that estimates the likelihood up to the current time point. Despite its theoretical appeal, this nested particle filter imposes substantial computational cost, limiting routine use in near-real-time outbreak response. We propose Ensemble SMC2 (eSMC2), a computationally efficient variant that replaces the inner particle filter with an Ensemble Kalman Filter (EnKF) to approximate the incremental likelihood at each observation time. While this substitution introduces bias via a Gaussian approximation, we mitigate finite-sample effects using an unbiased Gaussian density estimator and adapt the EnKF for epidemic data through state-dependent observation variance. This makes our approach particularly suitable for overdispersed incidence data commonly encountered in infectious disease surveillance. Simulation experiments with known ground truth and an application to 2022 United States (U.S.) monkeypox incidence data demonstrate that eSMC2 achieves substantial computational gains while producing posterior estimates comparable to SMC2. The method accurately recovers latent epidemic trajectories and key epidemiological parameters, providing an efficient framework for sequential Bayesian inference from imperfect surveillance data.Author summary: During infectious disease outbreaks, public health officials need timely estimates of how transmission is changing over time to make informed decisions about interventions. However, existing statistical methods for extracting these insights from noisy surveillance data are computationally demanding, which limits their practical use when rapid answers are needed. In this work, we developed a more efficient computational approach that substantially speeds up these calculations while maintaining reliable inference. Our method combines two established techniques: one that efficiently tracks how disease states evolve over time, and another that systematically updates parameter estimates as new data arrive. We demonstrate that our approach reliably recovers important epidemic features like time-varying transmission rates and the effective reproduction number from incomplete and uncertain case count data. By substantially reducing the computational burden, our method makes real-time monitoring more feasible during ongoing outbreaks, potentially enabling faster and more informed public health responses when decisions must be made quickly.