Epidemic threshold in structured scale-free networks.

By Víctor M. Eguíluz, K. Klemm. Physical Review Letters, 2002

332 citations recorded by the source corpus.

We analyze the spreading of viruses in scale-free networks with high clustering and degree correlations, as found in the Internet graph. For the susceptible-infected-susceptible model of epidemics the prevalence undergoes a phase transition at a finite threshold of the transmission probability. Comparing with the absence of a finite threshold in networks with purely random wiring, our result suggests that high clustering (modularity) and degree correlations protect scale-free networks against the spreading of viruses. We introduce and verify a quantitative description of the epidemic threshold based on the connectivity of the neighborhoods of the hubs.

Subfields: Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/745cda342e9eefeee7d131b04778c88e59fcdc31

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Citations in the corpus

The Effects of the Social Structure of Digital Networks on Viral Marketing Performance (2008, background): “Theoretical models of the spread of diseases and the absence of epidemic thresholds in scale-free networks are discussed at length in Boguna et al. (2003), Eguıluz and Klemm (2002), Moreno and Vázquez (2003), and Pastor-Satorras and Vespignani (2001).”
Patterns of Cascading Behavior in Large Blog Graphs (2007, background): “There is a huge literature on the study of epidemics on full cliques, homogeneous graphs, infinite graphs (see [13] for a survey), with recent studies on power-law networks [7] and arbitrary networks [21].”
Vital nodes identification in complex networks (2016, background): “These two algorithms are all based on the number of links among neighborhoods, while it is known that the local interconnectedness plays a negative role in the information spreading process [34, 35].”
Identifying Influential Nodes in Large-Scale Directed Networks: The Role of Clustering (2013, background): “The density of interactions among neighbors can be characterized by the local clustering coefficient [21], which has great impacts on network dynamics, such as game theory [12,13,22–24], cascading [25], synchronization [26,27] and spreading [28–31].”
Extremal Properties of Random Structures (2003, neutral): “aph becomes infected for arbitrarily low transmission probabilities [11, 39, 34]. The presence of additional network structure was found to further inﬂuence the spread of disease on scale-free graphs [16, 47, 33]. There are, however, diﬀerences between information ﬂows and the spread of viruses. Whi”
Information diffusion through blogspace (2004, background): “Egu´iluz and Klemm [10] have demonstrated a non-zero epidemic threshold under the SIS model in power-law networks produced by a certain generative model that takes into account the high clustering coef.cient the probability that two neighbors of a node are themselves neighbors found in real socia”
Networks and the Epidemiology of Infectious Disease (2010, background): “More recently, mean field solutions of the SIS model on networks have shown that both the speed and extent of an epidemic are dependent on the correlation pattern of the substrate network [91, 92].”
Graph theory and networks in Biology. (2006, methodology): “In [244] the SIS model was studied on a class of highly-clustered scale-free networks.”
The Structure and Function of Complex Networks (2003, background): “In particular, there may be a nonzero percolation threshold for certain types of correlations between vertices [56–59, 301, 400], if the network is embedded in a low-dimensional (rather than infinitedimensional) space [359, 408], or if the network has high transitivity [139] (see Sec.”