Physics-Informed Neural Networks for Infectious Disease Modeling with Limited Data
Jiwen Xia, Yineng Gao, Qi Tan, Yue Peng, Benyun Shi · 2024
Effective control of infectious diseases is crucial for public health decision making. Traditional infectious disease models, such as the SIR, SEIR, and SIDR models, face challenges during the early stages of an epidemic when data are scarce, epidemiological parameters are uncertain, and information is not immediately available. These limitations can hinder the accurate estimation of model parameters and reliable transmission predictions. To address these challenges, we introduce a Physics-Informed Neural Network (PINN) that integrates classical differential equations of infectious disease dynamics with neural networks. This approach enables the estimation of model parameters using a limited number of data points. As additional data become available, we incorporate incremental learning to capture evolving patterns and enhance both fitting and prediction accuracy. We tested this approach on classical infectious disease models, that is, SEIR, SIR, and SIDR. Our results demonstrate that PINN requires only a few data points to accurately estimate key parameters, including fixed and time-varying ones. Incorporating incremental learning allows models to adapt to changing patterns, thereby improving efficiency and performance. These findings underscore the potential of PINN as a robust tool for modeling infectious diseases, effectively combining physical laws with data-driven insights to enhance predictive capabilities.