Communicable diseases 'flow' between locations. These flows dictate where and when certain communities will be affected. While the prediction of disease flows is essential for the timely intervention of epidemics, few studies have addressed this critical issue. This study predicts disease flows during an epidemic by considering the epidemiological, network, and temporal contextual factors using a deep learning approach. A series of scenario analyses helps identify the effects of these contextual factors on disease flows. Results show that the extended spatial-temporal effect of the epidemiological factors stimulates disease flows. The compound effects of the network factors enhance the transmission efficiency of these flows. Lastly, the temporal effect accelerates the combined effects of epidemiological and network factors on the flows. Findings of this study reveal the intricate nature of disease flows and lay a solid foundation for real-time surveillance of epidemics and pandemics to inform timely interventions for a broad range of communicable diseases.