This paper proposes a sequential ensemble methodology for epidemic modeling that integrates discrete-time Hawkes processes (DTHP) and Susceptible-Exposed-Infectious-Removed (SEIR) models. Motivated by the need for accurate and reliable epidemic forecasts to inform timely public health interventions, we develop a flexible model averaging (MA) framework using Sequential Monte Carlo Squared. While generating estimates from each model individually, our approach dynamically assigns them weights based on their incrementally estimated marginal likelihoods, accounting for both model and parameter uncertainty, to produce a single ensemble estimate. We assess the methodology through simulation studies mimicking abrupt changes in epidemic dynamics, followed by an application to the Irish influenza and COVID-19 epidemics. Our results show that combining the two models can improve both estimates of the infection trajectory and reproduction number compared to using either model alone. Moreover, the MA consistently produces more stable and informative estimates of the time-varying reproduction number, with credible intervals that provide a realistic assessment of uncertainty. These features are particularly useful when epidemic dynamics change rapidly, enabling more reliable short-term forecasts and timely public health decisions. This research contributes to pandemic preparedness by enhancing forecast reliability and supporting more informed public health responses.

翻译：本文提出了一种用于流行病建模的顺序集成方法，该方法整合了离散时间霍克斯过程（DTHP）与易感-潜伏-感染-移除（SEIR）模型。受对准确可靠流行病预测以指导及时公共卫生干预的需求驱动，我们利用平方序列蒙特卡洛方法开发了一个灵活的模型平均框架。在分别从每个模型生成估计的同时，我们的方法根据其增量估计的边缘似然度动态分配权重，同时考虑模型和参数的不确定性，以产生单一的集成估计。我们通过模拟研究评估该方法，模拟了流行病动态的突变，随后将其应用于爱尔兰流感和COVID-19疫情。我们的结果表明，与单独使用任一模型相比，结合两种模型可以改善对感染轨迹和基本再生数的估计。此外，模型平均法持续产生更稳定且信息量更大的时变基本再生数估计，其可信区间提供了对不确定性的现实评估。这些特性在流行病动态快速变化时尤其有用，能够实现更可靠的短期预测和及时的公共卫生决策。本研究通过提升预测可靠性并支持更明智的公共卫生应对措施，为防范大流行病做出了贡献。