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 (SMC$^2$) 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 SMC$^2$ (eSMC$^2$), 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 eSMC$^2$ achieves substantial computational gains while producing posterior estimates comparable to SMC$^2$. The method accurately reconstructs epidemic trajectories and estimates key epidemiological parameters, providing an efficient framework for sequential Bayesian inference from imperfect surveillance data.

翻译：从部分观测、含噪声数据中估计潜在流行病状态与模型参数，仍是传染病建模领域的主要挑战。状态空间模型为此类推断提供了连贯的概率框架，但完全贝叶斯估计往往因需要积分潜在轨迹以评估观测数据似然，而面临计算负担过重的问题。序贯蒙特卡洛平方算法提供了一种用于联合状态与参数推断的严谨方法，其通过外层参数SMC采样器与内层粒子滤波器（估计截至当前时间点的似然值）相结合。尽管具有理论优势，这种嵌套粒子滤波器仍带来显著计算成本，限制了其在近实时疫情响应中的常规应用。我们提出集成SMC²（eSMC²），这是一种计算高效算法，通过集成卡尔曼滤波器替代内层粒子滤波器，以近似每个观测时刻的增量似然。虽然这种替代因高斯近似引入了偏差，但我们通过无偏高斯密度估计器缓解有限样本效应，并基于状态相关观测方差调整EnKF以适应流行病数据。该方法特别适用于传染病监测中常见的过度离散发病率数据。基于已知真实值的仿真实验及2022年美国猴痘发病率数据应用表明，eSMC²在保持与SMC²相当的参数后验估计质量的同时，实现了显著的计算效率提升。该方法能精确重构流行病轨迹并估计关键流行病学参数，为基于不完善监测数据的序贯贝叶斯推断提供了高效框架。