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

TL;DR

This paper introduces a sequential ensemble method combining Hawkes and SEIR models via SMC$^2$ to improve epidemic forecasting accuracy and reliability, especially during rapid epidemic changes.

Contribution

It develops a flexible model averaging framework that dynamically weights models based on marginal likelihoods, integrating model and parameter uncertainty for better epidemic estimates.

Findings

Ensemble approach improves infection trajectory estimates.

More stable and informative reproduction number estimates.

Enhanced short-term forecast reliability during dynamic epidemics.

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 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.