Physics-informed deep learning for infectious disease forecasting

Accurate forecasting of contagious diseases is critical for public health policymaking and pandemic preparedness. We propose a new infectious disease forecasting model based on physics-informed neural networks (PINNs), an emerging scientific machine learning approach. By embedding a compartmental model into the loss function, our method integrates epidemiological theory with data, helping to prevent model overfitting. We further enhance the model with a sub-network that accounts for covariates such as mobility and cumulative vaccine doses, which influence the transmission rate. Using state-level COVID-19 data from California, we demonstrate that the PINN model accurately predicts cases, deaths, and hospitalizations, aligning well with existing benchmarks. Notably, the PINN model outperforms naive baseline forecasts and several sequence deep learning models, including Recurrent Neural Networks (RNNs), Long Short-Term Memory (LSTM) networks, Gated Recurrent Units (GRUs), and Transformers. It also achieves performance comparable to a sophisticated Gaussian infection state forecasting model that combines compartmental dynamics, a data observation model, and parameter regression. However, the PINN model features a simpler structure and is easier to implement. In summary, we systematically evaluate the PINN model's ability to forecast infectious disease dynamics, demonstrating its potential as an efficient computational tool to strengthen forecasting capabilities.