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Predicting the epidemic threshold of the susceptible-infected-recovered model.

Wang W, Liu QH, Zhong LF, Tang M, Gao H, Stanley HE - Sci Rep (2016)

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.

View Article: 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.


Verify the accuracy for three types of theoretical epidemic threshold on real-world networks.The theoretical predictions of  (gray squares),  (red circles) and  (blue up triangles) versus numerical predictions λc of the epidemic threshold on (a) LHNs and (b) LKNs. (c) In the collective of LHNs and LKNs of real-world networks, the fraction of  [ or ] is the closest value to λc. (d) The values of  for LHNs and 〈k2〉/〈k〉 for LKNs versus the leading eigenvalue ΛA of the adjacent matrix.
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f4: Verify the accuracy for three types of theoretical epidemic threshold on real-world networks.The theoretical predictions of (gray squares), (red circles) and (blue up triangles) versus numerical predictions λc of the epidemic threshold on (a) LHNs and (b) LKNs. (c) In the collective of LHNs and LKNs of real-world networks, the fraction of [ or ] is the closest value to λc. (d) The values of for LHNs and 〈k2〉/〈k〉 for LKNs versus the leading eigenvalue ΛA of the adjacent matrix.

Mentions: Recent research results indicate that networks have distinct eigenvector localizations44. In real-world networks they are either localized on hubs networks (LHNs) or localized on k-core networks (LKNs). Depending on the localization of the eigenvector of adjacent matrix, there are 19 LHNs and 37 LKNs among the 56 real-world networks. Figure 4(d) shows that the values ΛA of LHNs are close to (blue squares), and the values ΛA of LKNs are close to 〈k2〉/〈k〉 (red circles). In LHNs [see Fig. 4(a,c)] the three methods perform as we would expect. The DMP method is the best predictor and the MFL method the worst because it neglects much detailed network structure information. In contrast, in the LKNs [see Fig. 4(b,c)], the simple MFL method performs the best, and it is slightly accurate than the DMP method.


Predicting the epidemic threshold of the susceptible-infected-recovered model.

Wang W, Liu QH, Zhong LF, Tang M, Gao H, Stanley HE - Sci Rep (2016)

Verify the accuracy for three types of theoretical epidemic threshold on real-world networks.The theoretical predictions of  (gray squares),  (red circles) and  (blue up triangles) versus numerical predictions λc of the epidemic threshold on (a) LHNs and (b) LKNs. (c) In the collective of LHNs and LKNs of real-world networks, the fraction of  [ or ] is the closest value to λc. (d) The values of  for LHNs and 〈k2〉/〈k〉 for LKNs versus the leading eigenvalue ΛA of the adjacent matrix.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4835734&req=5

f4: Verify the accuracy for three types of theoretical epidemic threshold on real-world networks.The theoretical predictions of (gray squares), (red circles) and (blue up triangles) versus numerical predictions λc of the epidemic threshold on (a) LHNs and (b) LKNs. (c) In the collective of LHNs and LKNs of real-world networks, the fraction of [ or ] is the closest value to λc. (d) The values of for LHNs and 〈k2〉/〈k〉 for LKNs versus the leading eigenvalue ΛA of the adjacent matrix.
Mentions: Recent research results indicate that networks have distinct eigenvector localizations44. In real-world networks they are either localized on hubs networks (LHNs) or localized on k-core networks (LKNs). Depending on the localization of the eigenvector of adjacent matrix, there are 19 LHNs and 37 LKNs among the 56 real-world networks. Figure 4(d) shows that the values ΛA of LHNs are close to (blue squares), and the values ΛA of LKNs are close to 〈k2〉/〈k〉 (red circles). In LHNs [see Fig. 4(a,c)] the three methods perform as we would expect. The DMP method is the best predictor and the MFL method the worst because it neglects much detailed network structure information. In contrast, in the LKNs [see Fig. 4(b,c)], the simple MFL method performs the best, and it is slightly accurate than the DMP method.

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.

View Article: 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.