Physics-guided framework for climate dependent disease prediction: coupling compartment model with deep learning

Influenza-like illness (ILI) serves as a representative climate dependent disease due to its climate sensitivity, widespread transmission, and significant impact on public health and societal functioning, highlighting the urgent need for reliable ILI prediction techniques that combine climate factors to support effective prevention and intervention. Existing compartmental model-based methods have limited ability to incorporate climate data and often struggle to capture the complex ILI transmission patterns. Many deep learning models generally lack interpretability and tend to overlook the interactions between climatic factors and ILI transmission. This study aims to develop a physics-guided framework that leverages the dynamical knowledge embedded in compartmental models and the multi-source data learning and representation capabilities of deep learning.

Our materials are the ILI case and climate data from Lanzhou, Gansu Province, China from 1st January 2023 to 26th October 2024 and Xi'an, Shaanxi Province, China from 1st January 2010 to 10th November 2016. Regarding the proposed model, first, we employ a physics-informed neural network (PINN) to learn the underlying dynamical knowledge under differential equation constraints and embed it into a long short-term memory network (LSTM) through a physics-guided representation alignment mechanism. Then, the transferred dynamical knowledge guides the LSTM to learn the mapping from climate and case data to ILI dynamics, enabling more accurate predictions jointly driven by domain knowledge and multi-source data.

The results demonstrate that the proposed framework generally achieves better prediction accuracy and trend consistency than five advanced baselines. Specifically, compared with suboptimal baselines in Lanzhou, our model achieves reductions of at least 21.81%, 20.76%, 21.86%, and 19.44% in NRMSE, SMAPE, ND, and MAPE, respectively, while improving PCC by at least 14.96%. In addition, we derive explicit functional relationships between transmission rates and climate factors via symbolic regression, and verify the effectiveness and reliability of the model by statistical test and ablation study.

The study finds that physics-guided representation alignment mechanism not only offers the potential to enhance ILI prediction under varying climatic conditions but also provides new insights and methodological support for epidemic prediction.