EpiRDN: A Learnable Anisotropic Reaction-Diffusion Network for Epidemic Time Series Prediction

Epidemic spread on graphs involves local infection dynamics and directional propagation through population movement. Current epidemic graph neural networks combine these aspects using a single symmetric aggregation operator, which limits the learning of their distinct timescales and fails to capture the asymmetry of real epidemic spread. This leads to node representations collapsing to a common state, losing diversity necessary for distinguishing infection stages. To address these issues, we propose EpiRDN, which discretizes the reaction-diffusion equation on graphs and learns its components end-to-end. EpiRDN features a local reaction network for region-level transitions and an anisotropic diffusion operator that utilizes asymmetric attention for directional infection flow. A feature-conditioned damping coefficient balances preserving local identity and neighborhood aggregation. We demonstrate that feature diversity in EpiRDN decays at most geometrically with depth, providing a significant advantage over existing methods. Experiments on four real-world datasets related to influenza and COVID-19 show consistent improvements, especially at longer forecasting horizons.