Solving stiff syndemic dynamics: A Climate-Integrated Physics-Informed Neural Network Reveals Hidden Malaria-Dengue Coinfections

The syndemic convergence of Malaria and Dengue represents a complex nonlinear system characterized by extreme time-scale separation. Modeling this interaction presents a formidable computational challenge due to the high stiffness ratio (S≫1) between slow seasonal vector evolution and rapid, high-frequency coinfection spikes. Conventional numerical integrators (e.g., Livermore Solver for Ordinary Differential Equations [LSODA]) frequently destabilize in these regimes, while pure data-driven deep learning (e.g., Long Short-Term Memory [LSTM] networks) suffers from dimensional collapse, failing to reconstruct latent states absent from training data. In this study, we propose a Climate-Integrated Physics-Informed Neural Network (CI-PINN) that integrates environmental forcing directly into a stiff SEIIR-C differential system. Utilizing a novel Curriculum Learning strategy to overcome spectral bias, the framework autonomously decouples low-frequency endemic manifolds from high-frequency stiff dynamics. A 4-way benchmark demonstrates that the CI-PINN reduces reconstruction error by orders of magnitude (Mean Squared Error [MSE] ≈8.5×10−5) compared to classical solvers, uniquely recovering the inferred 3D nonlinear attractor of the coinfection trajectory (R2>0.98). Biologically, the model identifies a transcritical bifurcation at 10.85 °C which aligns with the vector critical thermal minimum (CTmin) and further infers a potential cumulative hidden burden of 4903 coinfection cases during the October window, with an estimated peak weekly intensity of 1401 active cases. These findings suggest that current protocols underestimate the dual-disease load by approximately 15% under model assumptions, highlighting the critical role of physics-informed learning in resolving stiff biological dynamics.