arXiv:2601.09811v2 Announce Type: replace Abstract: We study data-driven learning of ecological and epidemic dynamics governed by nonlinear reaction and reaction--diffusion systems. We consider both neural approaches for learning the underlying reaction dynamics from trajectory data and Sparse Identification of Nonlinear Dynamics (SINDy) for discovering sparse, interpretable governing equations. A key component of this work is a partial-learning framework for reaction--diffusion systems. The prescribed diffusion operator is projected onto a reduced-order space and explicitly retained during differentiable integration, while only the unknown local eco-epidemic reaction is learned. This enables efficient training on fine spatial grids by evaluating the neural reaction only at a small set of informative nodes. The reduced solution is then reconstructed on the original fine grid and evaluated over both the training interval and an unseen future prediction horizon. Finally, the learned neural reaction is processed by SINDy to recover a sparse, interpretable symbolic model of the underlying dynamics. Experiments with clean and noisy data demonstrate high predictive accuracy, implicit denoising, computational efficiency, and the ability to recover sparse reaction models.