Localization and Spreading of Diseases in Complex Networks

Abstract

Using the susceptible-infected-susceptible model on unweighted and weighted networks, we consider the disease localization phenomenon. In contrast to the well-recognized point of view that diseases infect a finite fraction of vertices right above the epidemic threshold, we show that diseases can be localized on a finite number of vertices, where hubs and edges with large weights are centers of localization. Our results follow from the analysis of standard models of networks and empirical data for real-world networks.

Rare regions of the susceptible-infected-susceptible model on Barabási-Albert networks

“…[31] by analyzing spectral data of different graphs via finite size scaling. In particular, numerical evidence is shown for the disappearance of λ c with the expected scaling law in the N → ∞ limit.…”

“…Right above λ c similar concave shaped ρ(λ) was obtained as in the localized cases of Ref. [31]. Here I investigate the situation for SIS instead of CP models, to see if this relation holds on.…”

“…On the other hand, when f ( 1 ) is delocalized, the disease infects a finite fraction of vertexes for λ > λ c . Goltsev et al [31] analyzed artificial and real SF networks and found that in the case of localized cases, the epidemic threshold was actually absent and a real epidemic affecting a finite fraction of vertexes occurred after a smooth crossover at higher values of λ. This is in agreement with the smeared phase transition scenario proposed to explain the numerical results for CP on weighed BA trees in Ref.…”

“…The QMF approach is based on the rate equation for ρ i (t), the infection probability of node i at time t [31]:…”

“…I continue the work [30] to explore whether quenched mean-field (QMF) theory [31] with spectral decomposition (SD) can help understanding rare-region effects in complex networks. The QMF differs from HMF by taking into account variations of the quenched network topology.…”