Predicting the epidemic threshold of the susceptible-infected-recovered model.
Bottom Line:
When these methods are applied to predict epidemic threshold they often produce differing results and their relative levels of accuracy are still unknown.We systematically analyze these two issues-relationships among differing results and levels of accuracy-by studying the susceptible-infected-recovered (SIR) model on uncorrelated configuration networks and a group of 56 real-world networks.We find that in most of the networks with positive degree-degree correlations, an eigenvector localized on the high k-core nodes, or a high level of clustering, the epidemic threshold predicted by the MFL method, which uses the degree distribution as the only input information, performs better than the other two methods.
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PubMed Central - PubMed
Affiliation: Web Sciences Center, University of Electronic Science and Technology of China, Chengdu 610054, China.
ABSTRACT
Researchers have developed several theoretical methods for predicting epidemic thresholds, including the mean-field like (MFL) method, the quenched mean-field (QMF) method, and the dynamical message passing (DMP) method. When these methods are applied to predict epidemic threshold they often produce differing results and their relative levels of accuracy are still unknown. We systematically analyze these two issues-relationships among differing results and levels of accuracy-by studying the susceptible-infected-recovered (SIR) model on uncorrelated configuration networks and a group of 56 real-world networks. In uncorrelated configuration networks the MFL and DMP methods yield identical predictions that are larger and more accurate than the prediction generated by the QMF method. As for the 56 real-world networks, the epidemic threshold obtained by the DMP method is more likely to reach the accurate epidemic threshold because it incorporates full network topology information and some dynamical correlations. We find that in most of the networks with positive degree-degree correlations, an eigenvector localized on the high k-core nodes, or a high level of clustering, the epidemic threshold predicted by the MFL method, which uses the degree distribution as the only input information, performs better than the other two methods. No MeSH data available. |
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Mentions: We now compare the accuracy between the three theoretical epidemic thresholds under different microscopic and mesoscale topologies of real-world structures, including degree-degree correlations r, clustering c, and modularity Q. To measure the accuracy of the three methods in each theoretical prediction, we compute the average relative errors in the interval (x − Δx/2, x + Δx/2), where x is r, c, and Q. Here we set Δx = 0.1 unless otherwise specified. Figure 5(a,b) show that in all cases except the Facebook (NIPS) network the DMP method has a lower relative error when the Pearson correlation coefficient value is r < 0. The Facebook (NIPS) network may be an exception because the IPR value of its non-backtracking matrix is relatively large, i.e., 0.012. When r < 0, we can conclude that the DMP method performs the best and the MFL method performs the worst. When r > 0, the MFL method is the most accurate and the QMF method is the least. Figure 5(c–f) show the 56 real-world networks, separating them according to eigenvector localization. In LHNs we see a phenomenon similar to that shown in Fig. 5(a,b), i.e., when r < 0 the DMP method is the most accurate and the MFL method is the least, but when r > 0 the MFL method is the most accurate and the QMF method is the least. In LKNs, when r < 0 the DMP method is the most accurate, when r > 0 the MFL method is the most accurate, and the QMF method is always the least accurate. This suggests that the MFL method is the best for predicting epidemic thresholds in networks with positive degree-degree correlations, but that the DMP method is better in all other cases. |
View Article: PubMed Central - PubMed
Affiliation: Web Sciences Center, University of Electronic Science and Technology of China, Chengdu 610054, China.
No MeSH data available.