The spindle approximation of network epidemiological modeling

Understanding the dynamics of spreading and diffusion on networks is of critical importance for a variety of processes in real life. However, predicting the temporal evolution of diffusion on networks remains challenging as the process is shaped by network topology, spreading non-linearities, and heterogeneous adaptation behavior. In this study, we propose the ‘spindle vector’, a new network topological feature, which shapes nodes according to the distance from the root node. The spindle vector captures the relative order of nodes in diffusion propagation, thus allowing us to approximate the spatiotemporal evolution of diffusion dynamics on networks. The approximation simplifies the detailed connections of node pairs by only focusing on the nodal count within individual layers and the interlayer connections, seeking a compromise between efficiency and complexity. Through experiments on various networks, we show that our method outperforms the state-of-the-art on BA networks with an average improvement of 38.6% on the mean absolute error. Additionally, the predictive accuracy of our method exhibits a notable convergence with the pairwise approximation approach with the increasing presence of quadrangles and pentagons in WS networks. The new metric provides a general and computationally efficient approach to predict network diffusion problems and is of potential for a large range of network applications.