title: Numerical identification of epidemic thresholds for susceptible-infected-recovered model on finite-size networks.
abstract: Epidemic threshold has always been a very hot topic for studying epidemic dynamics on complex networks. The previous studies have provided different theoretical predictions of the epidemic threshold for the susceptible-infected-recovered (SIR) model, but the numerical verification of these theoretical predictions is still lacking. Considering that the large fluctuation of the outbreak size occurs near the epidemic threshold, we propose a novel numerical identification method of SIR epidemic threshold by analyzing the peak of the epidemic variability. Extensive experiments on synthetic and real-world networks demonstrate that the variability measure can successfully give the numerical threshold for the SIR model. The heterogeneous mean-field prediction agrees very well with the numerical threshold, except the case that the networks are disassortative, in which the quenched mean-field prediction is relatively close to the numerical threshold. Moreover, the numerical method presented is also suitable for the susceptible-infected-susceptible model. This work helps to verify the theoretical analysis of epidemic threshold and would promote further studies on the phase transition of epidemic dynamics.
authors.affiliation: Web Sciences Center, University of Electronic Science and Technology of China, Chengdu 610054, China.
authors.forename: Panpan
authors.initials: P
authors.lastname: Shu
authors.affiliation: Web Sciences Center, University of Electronic Science and Technology of China, Chengdu 610054, China.
authors.forename: Wei
authors.initials: W
authors.lastname: Wang
authors.affiliation: Web Sciences Center, University of Electronic Science and Technology of China, Chengdu 610054, China.
authors.forename: Ming
authors.initials: M
authors.lastname: Tang
authors.affiliation: Department of Mathematics, Kyungpook National University, Daegu 702-701, South Korea.
authors.forename: Younghae
authors.initials: Y
authors.lastname: Do
mesh_terms: D000818:Animals; D003198:Computer Simulation; D006801:Humans; D007239:Infections / Q000453:epidemiology*; D008954:Models, Biological