A sequential ensemble approach to epidemic modeling: Combining Hawkes and SEIR models using SMC$^2$

2025-06-18

AI Summary

To address low accuracy and poor robustness in epidemic trajectory forecasting and time-varying effective reproduction number (Rₜ) estimation, this paper proposes a sequential Bayesian model averaging framework based on the SMC² algorithm, which— for the first time—integrates a discrete-time Hawkes process with an SEIR model. The method dynamically weights predictions from both models, explicitly jointly accounting for both structural and parametric uncertainty, and adaptively allocates weights via marginal likelihood. Experiments on real-world influenza and COVID-19 data demonstrate that the proposed approach significantly improves accuracy in infection trajectory and Rₜ estimation; yields Rₜ credible intervals with coverage closer to nominal levels; reduces estimation volatility; and exhibits superior stability during abrupt epidemiological turning points.

Technology Category

• Reasoning under Uncertainty: Sequential Decision Making
• Intelligent Robots: State Estimation
• Machine Learning: Calibration & Uncertainty Quantification

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

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 outbreaks. 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 maintain appropriate coverage. These features are particularly valuable in high-uncertainty contexts where reliable situational awareness is essential. This research contributes to pandemic preparedness by enhancing forecast reliability and supporting more informed public health responses.

Problem

• Integrate Hawkes and SEIR models for better epidemic forecasts
• Dynamically weight models to handle uncertainty in predictions
• Improve infection trajectory and reproduction number estimates

Innovation

• Combines Hawkes and SEIR models dynamically
• Uses Sequential Monte Carlo Squared for weights
• Improves infection trajectory and reproduction estimates