Physics-Informed GNN Epidemic Forecasting via Double-Layer Dynamic Model

Online social networks serve as an essential platform for human behavior, making the exploration of their impact on epidemic spread a significant issue. This study utilizes the research methodology of propagation dynamics to quantify the interaction between information dissemination in social networks and virus diffusion in physical networks. The double-layer dynamic model was constructed, introducing the concept of dynamic transmission probabilities. The dynamic infection probability of disease transmission incorporates the information immunization effect, where wide-spread information dissemination leads to spontaneous immune behavior among the population. The dynamic transmission probability of information spread incorporates the fear effect, where a surge in mortality rates triggers exponential information dissemination. Mathematical derivations, parameter analyses, and simulation experiments were initially conducted. Subsequently, the differential equations of the double-layer network dynamic model were used to propose the new double-layer dynamic module. Thus, this article proposes a novel epidemic forecasting framework called physics-informed graph neural network (PIGNN). Extensive experiments show that our proposed PIGNN model outperforms the state-of-the-art method. Meanwhile, the double-layer network dynamic model was demonstrated to capture real-world phenomena vividly.