Recent pandemics have highlighted the critical role of infectious disease models in guiding public health decision-making, driving demand for realistic models that can provide timely answers under uncertainty. Compartmental models are widely used to capture disease dynamics, and advances in data availability, computational resources, and epidemiological understanding have allowed the development of models that incorporate detailed representations of population structure, disease progression, and intervention effects. While these improvements improve model fidelity, they also increase model complexity, leading to high-dimensional parameter spaces, intractable likelihoods, and computational challenges for fitting models to limited surveillance data in real time. Existing likelihood-free methods, such as Approximate Bayesian Computation (ABC) and Bayesian Synthetic Likelihood (BSL), have developed largely independently, each with distinct strengths and limitations. We propose an integrated three-stage framework that synthesizes advances from both likelihood-based and likelihood-free method: (1) ABC-based entropy minimization to identify low-dimensional, approximately orthogonal summary statistics; (2) BSL inference using these optimized summaries to construct tractable Gaussian approximations; and (3) Hamiltonian Monte Carlo sampling for efficient posterior exploration. Through SEIR simulation study and application to the 1978 British boarding school influenza outbreak, we demonstrate that our framework achieves reliable parameter estimation and uncertainty quantification while maintaining computational efficiency.

翻译：近期的大流行凸显了传染病模型在指导公共卫生决策中的关键作用，推动了人们对能够在不确性下提供及时响应的现实模型的需求。房室模型广泛用于描述疾病动态，数据可用性、计算资源和流行病学理解的进步使得模型能够纳入人口结构、疾病进展和干预效应的详细表示。虽然这些改进提高了模型保真度，但也增加了模型复杂性，导致参数空间高维、似然函数难解，并对基于有限监测数据实时拟合模型带来了计算挑战。现有的无似然方法，如近似贝叶斯计算（ABC）和贝叶斯合成似然（BSL），在很大程度上是独立发展的，各自具有独特的优势和局限性。我们提出了一种集成的三阶段框架，综合了基于似然和无似然方法的进展：（1）基于ABC的熵最小化，以识别低维、近似正交的汇总统计量；（2）使用这些优化的汇总统计量进行BSL推断，以构建可处理的 Gaussian 近似；（3）使用哈密顿蒙特卡洛采样进行高效的后验探索。通过SEIR仿真研究以及应用于1978年英国寄宿学校流感暴发案例，我们证明该框架能够在保持计算效率的同时，实现可靠的参数估计和不确定性量化。