Precisely identifying the epidemic thresholds in real networks via asynchronous updating

Two numerical simulation methods, asynchronous updating and synchronous updating, are applied to mimic epidemic spreading and identify epidemic threshold. As a continuous time Markov process, asynchronous updating makes only one node be selected to change its state in each time step, and thus reflects the fact that nodes are updated independently, which is more reasonable to describe the real dynamic process of disease spreading. Unlike previous studies based on prevalent synchronous updating, in this paper, we mainly apply asynchronous updating to precisely identify epidemic thresholds of SIR spreading dynamics in real networks. Meanwhile, we also use four benchmark theoretical methods, i.e., the heterogeneous mean-field (HMF), the quenched mean-field (QMF), the dynamical message passing (DMP) and the connectivity matrix (CM), to verify the identification accuracy based on asynchronous updating. The extensive numerical experiments in 41 real networks show that the identification accuracy approaches more closely to the theoretical results obtained from the CM because the CM incorporates network topology with dynamic correlations. In addition, because asynchronous updating is high time complexity comparing with synchronous updating, we further investigate the approximation of synchronous updating to asynchronous updating by modulating very small time step. When the time step of synchronous updating is set with 0.2, it can approach closely to the identification accuracy based asynchronous updating, and guarantee a lower time complexity.