The international aviation network has facilitated global population movement. This has not only significantly contributed to the cross-border spread of infectious diseases, but has also had substantial economic consequences worldwide during the pandemic. Thus, understanding the dynamic relationship between mobility, epidemic spread, and economic trends is crucial for informing more balanced and adaptive public health and economic policies. Existing models have a tendency to prioritize infection trends, neglecting to account for the nonlinear interplay between population mobility, epidemic spread, and economic fluctuations. We propose a hybrid model architecture that combines the graph sample and aggregate (GraphSAGE) algorithm for modeling spatial dependencies driven by population flow and Long Short-Term Memory (LSTM) for capturing temporal patterns of infections and economic indicators. The simulation results demonstrate the model's capacity to predict infection dynamics and economic trends accurately. These findings underscore the value of data-driven strategies in enabling timely public health responses and in supporting the formulation of coordinated cross-border mobility policies during global health emergencies.