Data-driven forecasting of Flu, RSV, and COVID-19 related outcomes in the United States and Canada via Hankel dynamic mode decomposition

The (large) season-to-season variability and limited dynamical history make the forecasting of infectious diseases a challenging problem. Here, we examine the extent to which advances in data-driven dynamical modeling can provide accurate predictions by benchmarking the performance of one such method, Hankel dynamic mode decomposition (DMD), on the 2024-2025 influenza, respiratory syncytial virus (RSV), and COVID-19 seasons in the United States and Canada. Using Hankel-DMD, we generated weekly forecasts that were submitted to the Center for Disease Control and Prevention's (CDC) FluSight Forecast Hub and the University of Guelph's AI4CastingHub. Across both Hubs, we find that Hankel-DMD can provide high quality forecasts at the beginning and end of the season, but forecasts in the middle of the season suffer from significant overestimation of the season peak. This leads to worse than baseline performance on FluSight Forecast Hub, when submissions are evaluated across the entire season. Hankel-DMD is found to be the best among a small number of models that submitted enough forecasts against which to compare for forecasting influenza, RSV, and COVID-19 in Canada. As this was the first active year of AI4CastingHub, this suggests that Hankel-DMD may be especially useful when expertise is lacking for predicting infectious dynamics in new regions. To study how Hankel-DMD can be better equipped to provide accurate forecasts during the season peak, we explored whether DMD with memory, a recently developed approach for applying DMD to non-stationary dynamical systems, provides significant improvements. Retrospective analysis using DMD with memory shows promise in reducing overestimation during season peak, but the extent to which its optimal use can be achieved in a live forecasting setting remains to be seen. Collectively, our results demonstrate that Hankel-DMD has potential as an efficient and interpretable method for the forecasting of infectious diseases, while also highlighting a number of remaining methodological challenges which future work should aim to address.