A simple yet effective approach for predicting disease spread using mathematically-inspired diffusion-informed neural networks

The COVID-19 outbreak has highlighted the importance of mathematical epidemic models like the Susceptible-Infected-Recovered (SIR) model, for understanding disease spread dynamics. However, enhancing their predictive accuracy complicates parameter estimation. To address this, we proposed a novel model that integrates traditional mathematical modeling with deep learning which has shown improved predicted power across diverse fields. The proposed model includes a simple artificial neural network (ANN) for regional disease incidences, and a graph convolutional neural network (GCN) to capture spread to adjacent regions. GCNs are a recent deep learning algorithm designed to learn spatial relationship from graph-structured data. We applied the model to COVID-19 incidences in Spain to evaluate its performance. It achieved a 0.9679 correlation with the test data, outperforming previous models with fewer parameters. By leveraging the efficient training methods of deep learning, the model simplifies parameter estimation while maintaining alignment with the mathematical framework to ensure interpretability. The proposed model may allow the more robust and insightful analyses by leveraging the generalization power of deep learning and theoretical foundations of the mathematical models.