Physics-informed deep learning for infectious disease forecasting

Accurate forecasting of contagious illnesses has become increasingly important to public health policymaking, and better prediction could prevent the loss of millions of lives. To better prepare for future pandemics, it is essential to improve forecasting methods and capabilities. In this work, we propose a new infectious disease forecasting model based on physics-informed neural networks (PINNs), an emerging area of scientific machine learning. The proposed PINN model incorporates dynamical systems representations of disease transmission into the loss function, thereby assimilating epidemiological theory and data using neural networks (NNs). Our approach is designed to prevent model overfitting, which often occurs when training deep learning models with observation data alone. In addition, we employ an additional sub-network to account for mobility, cumulative vaccine doses, and other covariates that influence the transmission rate, a key parameter in the compartmental model. To demonstrate the capability of the proposed model, we examine the performance of the model using state-level COVID-19 data in California. Our simulation results show that predictions of PINN model on the number of cases, deaths, and hospitalizations are consistent with existing benchmarks. In particular, the PINN model outperforms naive baseline forecasts and various sequence deep learning models, such as Recurrent Neural Networks (RNNs), Long Short-Term Memory (LSTM) networks, Gated Recurrent Units (GRUs), and Transformer models. We also show that the performance of the PINN model is comparable to a sophisticated Gaussian infection state forecasting model that combines the compartmental model, a data observation model and a regression model for inferring parameters in the compartmental model. Nonetheless, the PINN model offers a simpler structure and is easier to implement. In summary, we perform a systematic study of the predictive capability of the PINN model in forecasting the dynamics of infectious diseases and our results showcase the potential of the proposed model as an efficient computational tool to enhance the current capacity of infectious disease forecasting.