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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.


Effects of clustering on the relative errors of different theoretical prediction.In the first column, figures (a,c,e) are the the relative errors of the three different theoretical predictions versus clustering c. In the second column, figures (b,d,f) are the the average relative errors for the three different theoretical predictions versus c. The first row exhibits the results of 56 real-world networks, the second row shows the results of LHNs, the third row performs the results of the LKNs.
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f6: Effects of clustering on the relative errors of different theoretical prediction.In the first column, figures (a,c,e) are the the relative errors of the three different theoretical predictions versus clustering c. In the second column, figures (b,d,f) are the the average relative errors for the three different theoretical predictions versus c. The first row exhibits the results of 56 real-world networks, the second row shows the results of LHNs, the third row performs the results of the LKNs.

Mentions: Using an analytic framework similar to that shown in Fig. 5, we compare the accuracy among the three theoretical predictions under different clustering coefficient c in Fig. 6. Figure 6(a,b) show that when c < 0.1, the relative error of the DMP method is the lowest and the relative error of the MFL method is the largest. When c > 0.1, the relative error of the MFL method is the lowest and the relative error of the QMF method is, in most cases, the largest. Thus when c < 0.1 the DMP method is the most accurate in predicting the epidemic threshold, but when c > 0.1 the MFL method is the most accurate. In LHNs, we find the same phenomena as shown in Fig. 6(a,b). The DMP method is the best predictor when c < 0.1, and the MFL method the best when c > 0.1 [see Fig. 6(c,d)]. Figure 6(e,f) show that in LKNs the DMP method performs the best for small c and the MFL method the best for large c.


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)

Effects of clustering on the relative errors of different theoretical prediction.In the first column, figures (a,c,e) are the the relative errors of the three different theoretical predictions versus clustering c. In the second column, figures (b,d,f) are the the average relative errors for the three different theoretical predictions versus c. The first row exhibits the results of 56 real-world networks, the second row shows the results of LHNs, the third row performs the results of the LKNs.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

f6: Effects of clustering on the relative errors of different theoretical prediction.In the first column, figures (a,c,e) are the the relative errors of the three different theoretical predictions versus clustering c. In the second column, figures (b,d,f) are the the average relative errors for the three different theoretical predictions versus c. The first row exhibits the results of 56 real-world networks, the second row shows the results of LHNs, the third row performs the results of the LKNs.
Mentions: Using an analytic framework similar to that shown in Fig. 5, we compare the accuracy among the three theoretical predictions under different clustering coefficient c in Fig. 6. Figure 6(a,b) show that when c < 0.1, the relative error of the DMP method is the lowest and the relative error of the MFL method is the largest. When c > 0.1, the relative error of the MFL method is the lowest and the relative error of the QMF method is, in most cases, the largest. Thus when c < 0.1 the DMP method is the most accurate in predicting the epidemic threshold, but when c > 0.1 the MFL method is the most accurate. In LHNs, we find the same phenomena as shown in Fig. 6(a,b). The DMP method is the best predictor when c < 0.1, and the MFL method the best when c > 0.1 [see Fig. 6(c,d)]. Figure 6(e,f) show that in LKNs the DMP method performs the best for small c and the MFL method the best for large c.

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.