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

Weekly influenza surveillance counts guide vaccine distribution and public-health alerts, yet they are hard to forecast. Each region offers only a few seasons, waves shift in timing and height every year, and information that helps while a wave grows misleads after its peak, whereas last season's shape stays informative for a year. Existing epidemic graph models and general forecasters read a short fixed window and treat all past information alike, so they neither exploit earlier seasons nor discard stale associations when the epidemic phase changes. To address these limitations, we propose TERN, a forecaster built around a delta-rule fast-weight memory that decays channel-wise and erases along a learned address under gates driven by local epidemic-phase features, combined with an explicit seasonal reference and online adaptation. On three Cola-GNN influenza benchmarks, TERN outperformed epidemic graph models and general forecasters, matched or exceeded seasonal references, and a controlled comparison confirmed the contribution of the memory itself.