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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.


Comparing the accuracy between three types of theoretical and numerical predictions of the epidemic threshold on 56 real-world networks.(a) Theoretical predictions of  (gray squares),  (red circles) and  (blue up triangles) versus numerical predictions λc of the epidemic threshold. (b) In all the entire sample of real-world networks, the fraction of  [ or ] is the closest value to λc.
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f2: Comparing the accuracy between three types of theoretical and numerical predictions of the epidemic threshold on 56 real-world networks.(a) Theoretical predictions of (gray squares), (red circles) and (blue up triangles) versus numerical predictions λc of the epidemic threshold. (b) In all the entire sample of real-world networks, the fraction of [ or ] is the closest value to λc.

Mentions: Figure 2(a) shows the accuracy of , , and when applied to the 56 networks. Each symbol marks a theoretical prediction versus a numerical network prediction. We compute the relative frequency of , , and to determine which one produces a value closest to λc [see Fig. 2(b)]. Because the DMP method considers the full information of network topology and also some dynamical correlations, is the best prediction in more than 40% of the networks. The value is the closest to the actual epidemic threshold in 25% of the networks, and the epidemic threshold predicted by the MFL method, which uses the degree distribution as the only input parameter, is closest to the real epidemic threshold in about one-third of the real-world networks. Comparing these three predictions we find that the DMP method outperforms the other two, i.e., when determining the epidemic threshold in a general network, the DMP method is more frequently accurate than the other two.


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)

Comparing the accuracy between three types of theoretical and numerical predictions of the epidemic threshold on 56 real-world networks.(a) Theoretical predictions of  (gray squares),  (red circles) and  (blue up triangles) versus numerical predictions λc of the epidemic threshold. (b) In all the entire sample of real-world networks, the fraction of  [ or ] is the closest value to λc.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

f2: Comparing the accuracy between three types of theoretical and numerical predictions of the epidemic threshold on 56 real-world networks.(a) Theoretical predictions of (gray squares), (red circles) and (blue up triangles) versus numerical predictions λc of the epidemic threshold. (b) In all the entire sample of real-world networks, the fraction of [ or ] is the closest value to λc.
Mentions: Figure 2(a) shows the accuracy of , , and when applied to the 56 networks. Each symbol marks a theoretical prediction versus a numerical network prediction. We compute the relative frequency of , , and to determine which one produces a value closest to λc [see Fig. 2(b)]. Because the DMP method considers the full information of network topology and also some dynamical correlations, is the best prediction in more than 40% of the networks. The value is the closest to the actual epidemic threshold in 25% of the networks, and the epidemic threshold predicted by the MFL method, which uses the degree distribution as the only input parameter, is closest to the real epidemic threshold in about one-third of the real-world networks. Comparing these three predictions we find that the DMP method outperforms the other two, i.e., when determining the epidemic threshold in a general network, the DMP method is more frequently accurate than the other two.

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.