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.
Highlights
We find that the mean-field like (MFL) and dynamical message passing (DMP) methods predict the same epidemic threshold value for uncorrelated configuration networks and that this value is larger and more accurate than the value predicted by the quenched mean-field (QMF) method
We find that the relative and absolute errors between the theoretical and numerical predictions increase with inverse participation ratios (IPR), i.e., the QMF and DMP methods deviate from the accurate epidemic threshold more when IPR is large because the eigenvector centralities of adjacent and non-backtracking matrixes are localized on hub nodes or high k-core index nodes[44]
In this study we have systematically examined the accuracies and relationships among the MFL, QMF, and DMP methods for predicting the epidemic threshold in the SIR model
Summary
The theoretical approaches always assume (i) that an epidemic can spread on a large, sparse network[7,14,16,28], (ii) that dynamical correlations among the neighbors do not exist[7], and (iii) that all the nodes or edges within a given class are statistically equivalent[7,17] These three methods usually focus on a class of networks, such as uncorrelated networks, clustering networks, and community networks. In the 56 real-world networks studied, the DMP method performs the best in most cases because it considers the full topology and many of the dynamical correlations among the states of the neighbors, but due to the localized eigenvector of the adjacent matrix the QMF method often deviates from accurate epidemic threshold values. We note that the performances of the three predictions do not exhibit an obvious regularity versus the modularity, and in most cases the DMP method performs better than other two
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