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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.


The effects of inverse participation ratio (IPR) of the adjacency and the nonbacktracking matrices on the accuracy of theoretical predictions.(a) The relative errors and (b) absolute errors as a function of IPR of the principal eigenvectors of the adjacency (black squares) and the nonbacktracking matrices (red circles). The inset of (b) is the average absolute errors as a function of IPR.
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f3: The effects of inverse participation ratio (IPR) of the adjacency and the nonbacktracking matrices on the accuracy of theoretical predictions.(a) The relative errors and (b) absolute errors as a function of IPR of the principal eigenvectors of the adjacency (black squares) and the nonbacktracking matrices (red circles). The inset of (b) is the average absolute errors as a function of IPR.

Mentions: Theoretical predictions given by the MFL method often fail because it neglects much structural information and also all dynamical correlations. The performance of the QMF method is counterintuitive because of the localized eigenvector of the leading eigenvalue of the adjacent matrix [see Fig. 3(a)]. Figure 3 shows the effects of the inverse participation ratios (IPR)3945 of the adjacent and non-backtracking matrixes. We find that the relative and absolute errors between the theoretical and numerical predictions increase with IPR, i.e., the QMF and DMP methods deviate from the accurate epidemic threshold more easily when IPR is large because the eigenvector centralities of adjacent and non-backtracking matrixes are localized on hub nodes or high k-core index nodes44. The relative error of method u ∈ {MFL, QMF, DMP} can be .


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)

The effects of inverse participation ratio (IPR) of the adjacency and the nonbacktracking matrices on the accuracy of theoretical predictions.(a) The relative errors and (b) absolute errors as a function of IPR of the principal eigenvectors of the adjacency (black squares) and the nonbacktracking matrices (red circles). The inset of (b) is the average absolute errors as a function of IPR.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

f3: The effects of inverse participation ratio (IPR) of the adjacency and the nonbacktracking matrices on the accuracy of theoretical predictions.(a) The relative errors and (b) absolute errors as a function of IPR of the principal eigenvectors of the adjacency (black squares) and the nonbacktracking matrices (red circles). The inset of (b) is the average absolute errors as a function of IPR.
Mentions: Theoretical predictions given by the MFL method often fail because it neglects much structural information and also all dynamical correlations. The performance of the QMF method is counterintuitive because of the localized eigenvector of the leading eigenvalue of the adjacent matrix [see Fig. 3(a)]. Figure 3 shows the effects of the inverse participation ratios (IPR)3945 of the adjacent and non-backtracking matrixes. We find that the relative and absolute errors between the theoretical and numerical predictions increase with IPR, i.e., the QMF and DMP methods deviate from the accurate epidemic threshold more easily when IPR is large because the eigenvector centralities of adjacent and non-backtracking matrixes are localized on hub nodes or high k-core index nodes44. The relative error of method u ∈ {MFL, QMF, DMP} can be .

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.