TERN: A Delta-rule Memory with a Seasonal Reference and Online Adaptation for Epidemic Forecasting

Seasonal influenza infects millions of people and causes substantial morbidity and mortality in the United States each year, making accurate short-term forecasting a core public-health need. Reliable forecasts of epidemic time series can inform vaccination timing, hospital staffing, and resource allocation, yet the comparative behavior of modern forecasting architectures on infectious-disease surveillance data remains insufficiently characterized. We address this gap through a systematic evaluation of regional influenza forecasting using influenza-like illness surveillance and influenza-associated hospitalization time series under both temporal and spatial generalization settings for 1-4-week-ahead prediction. We compare classical neural network architectures, numerical transformer-based models, pretrained time series foundation models, and LLM-based forecasting approaches. Across tasks, we demonstrate that a mixture-of-experts model that fuses multiple pretrained forecasters achieves the strongest overall performance, indicating that heterogeneous pretrained representations provide complementary predictive information. Our results further show that numerical transformer-based models produce reliable forecasts, while pretraining provides the largest gains at longer horizons, particularly when the pretraining domain is mechanistically aligned with influenza dynamics. In contrast, LLM-based time series methods underperform relative to numerical forecasters in this setting. Finally, we examine hospitalization information as both an auxiliary covariate and a pretraining source. Hospitalization signals provide complementary improvements in selected settings and clarify when additional surveillance streams enhance the robustness of multi-horizon forecasting. These findings provide actionable guidance on model selection, pretraining strategy, and auxiliary-signal use for influenza preparedness.

Forecasting infectious disease incidence can provide important information to guide public health planning, yet is difficult because epidemic dynamics are complex. Current mechanistic and statistical approaches often struggle to capture multimodal uncertainty or emergent trends. Influpaint adapts denoising diffusion probabilistic models to epidemic forecasting. By encoding influenza seasons as spatiotemporal images in which pixel intensity represents incidence, Influpaint learns a rich distribution of disease dynamics from a hybrid dataset of surveillance and simulated trajectories. Forecasting is formulated as a conditional generation (inpainting) task from partial observations. We show that Influpaint generates realistic, diverse epidemic trajectories and achieves forecast accuracy that is competitive with leading ensemble methods in retrospective evaluation. In real-time evaluation during the 2023--2025 U.S. CDC FluSight challenges, performance improved substantially across seasons, with highly accurate but somewhat overconfident projections in 2024--2025. The best performance was achieved with a training dataset containing 30% surveillance and 70% simulated trajectories. These results show that diffusion models can capture important spatiotemporal structure in influenza dynamics and provide a flexible framework for probabilistic infectious disease forecasting.

Accurate multi-week dengue forecasting supports timely vector-control interventions, outbreak preparedness, and healthcare resource allocation. However, newly established surveillance systems often lack the historical data needed to train reliable neural forecasting models. Although pretrained time-series models offer promising zero-shot forecasts, their cross-domain training may not capture local epidemiological dynamics. We propose TREA-Net, a Transferable Residual Epidemiological Adaptation Network for dengue forecasting under limited data. TREA-Net augments neural forecasting backbones with projections from an Environmental Time-Series Susceptible-Infected-Recovered model and learns a lightweight gated residual correction transferable from data-rich to data-scarce regions. Its node-invariant design accommodates surveillance systems with different numbers of locations, while target adaptation requires learning only two global parameters. We transfer knowledge from long-running dengue surveillance in Colombia and Nicaragua to 8-week-ahead forecasting in Mexico and Malaysia using only 78 or 104 weeks of target data. Across five neural backbones and ten transfer settings, TREA-Net improves the corresponding backbone in 9 out of 10 settings, with statistically significant gains. When integrated with TiRex, a foundation model for forecasting, it achieves the lowest mean absolute error across all target datasets. Conformal prediction further maintains empirical coverage while reducing 8-week prediction-interval width by 29.6% in Mexico. These results demonstrate TREA-Net's potential as a lightweight and portable early-warning framework for health agencies with limited surveillance data.