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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.


Predicting epidemic threshold for uncorrelated configuration networks under different network sizes.Theoretical predictions of  (black solid lines),  (red dashed lines),  (blue dash-dotted lines) and numerical prediction (gray squares) versus network size N for degree exponent νD = 2.1 (a) and νD = 3.5 (b). The absolute errors between λc and  (black solid lines),  (red dashed lines) and  (blue dash-dotted lines) versus N for νD = 2.1 (c) and νD = 3.5 (d).
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f1: Predicting epidemic threshold for uncorrelated configuration networks under different network sizes.Theoretical predictions of (black solid lines), (red dashed lines), (blue dash-dotted lines) and numerical prediction (gray squares) versus network size N for degree exponent νD = 2.1 (a) and νD = 3.5 (b). The absolute errors between λc and (black solid lines), (red dashed lines) and (blue dash-dotted lines) versus N for νD = 2.1 (c) and νD = 3.5 (d).

Mentions: Figure 1 shows a systematic study of the SIR model on uncorrelated configuration networks. We focus on size N scale-free networks with power-law degree distributions, i.e., , where νD is the degree exponent. The minimum degree is kmin = 3, and the maximum degree kmax is set at , which ensures that there will be no degree-degree correlations in the thermodynamic limit. Without lack of generality, we can set γ = 1 in simulations. Two values, νD = 2.1 and νD = 3.5, are considered. According to definition44, networks with νD = 2.1 are LKNs and networks with νD = 3.5 are LHNs. Figure 1 shows that predictions from the MFL () and DMP () methods in general produce similar theoretical values and perform better than the prediction from the QMF () method. When νD = 2.1, the absolute errors in the epidemic threshold from the MFL and DMP methods are very small for all values of N, and the absolute errors from the QMF method decrease with N. The absolute error for method u ∈ {MFL, QMF, DMP} is . When νD = 3.5, the absolute error from the QMF method stabilizes to finite values even in infinitely large networks, and the absolute errors for the MFL and DMP methods decrease with N. From these results we find that the performance of the QMF method is counterintuitive, i.e., that its performance is even worse than the MFL method. At the same time, all of these results confirm the relationships among the three theoretical predictions for uncorrelated networks previously discussed.


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)

Predicting epidemic threshold for uncorrelated configuration networks under different network sizes.Theoretical predictions of  (black solid lines),  (red dashed lines),  (blue dash-dotted lines) and numerical prediction (gray squares) versus network size N for degree exponent νD = 2.1 (a) and νD = 3.5 (b). The absolute errors between λc and  (black solid lines),  (red dashed lines) and  (blue dash-dotted lines) versus N for νD = 2.1 (c) and νD = 3.5 (d).
© Copyright Policy - open-access
Related In: Results  -  Collection

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

f1: Predicting epidemic threshold for uncorrelated configuration networks under different network sizes.Theoretical predictions of (black solid lines), (red dashed lines), (blue dash-dotted lines) and numerical prediction (gray squares) versus network size N for degree exponent νD = 2.1 (a) and νD = 3.5 (b). The absolute errors between λc and (black solid lines), (red dashed lines) and (blue dash-dotted lines) versus N for νD = 2.1 (c) and νD = 3.5 (d).
Mentions: Figure 1 shows a systematic study of the SIR model on uncorrelated configuration networks. We focus on size N scale-free networks with power-law degree distributions, i.e., , where νD is the degree exponent. The minimum degree is kmin = 3, and the maximum degree kmax is set at , which ensures that there will be no degree-degree correlations in the thermodynamic limit. Without lack of generality, we can set γ = 1 in simulations. Two values, νD = 2.1 and νD = 3.5, are considered. According to definition44, networks with νD = 2.1 are LKNs and networks with νD = 3.5 are LHNs. Figure 1 shows that predictions from the MFL () and DMP () methods in general produce similar theoretical values and perform better than the prediction from the QMF () method. When νD = 2.1, the absolute errors in the epidemic threshold from the MFL and DMP methods are very small for all values of N, and the absolute errors from the QMF method decrease with N. The absolute error for method u ∈ {MFL, QMF, DMP} is . When νD = 3.5, the absolute error from the QMF method stabilizes to finite values even in infinitely large networks, and the absolute errors for the MFL and DMP methods decrease with N. From these results we find that the performance of the QMF method is counterintuitive, i.e., that its performance is even worse than the MFL method. At the same time, all of these results confirm the relationships among the three theoretical predictions for uncorrelated networks previously discussed.

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.