Viral conductance: Quantifying the robustness of networks with respect to spread of epidemics

Youssef, Mina; Kooij, Robert E.; Scoglio, Caterina

doi:10.1016/j.jocs.2011.03.001

Cited by 37 publications

(32 citation statements)

References 29 publications

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“…The more irregular a graph is, the smaller the slope, which agrees with simulations in [14]. Further, the inequality shows that slope decreases at least as fast as τ c = 1 λ1…”

Section: -P3supporting

confidence: 85%

“…This means that a higher effective infection rate τ is needed to cause a non-zero steady-state fraction of nodes in the regular graph to be permanently infected, but that, slightly above that critical rate τ c ,ah i g h e rr e l a t i v e fraction of nodes is infected than in other graphs. In other words, the change in virus conductivity [14] at τ = τ c + ǫ is highest in regular graphs.…”

Section: -P3mentioning

confidence: 97%

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Epidemic phase transition of the SIS type in networks

Mieghem

2012

EPL

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-By making only one approximation of a mean-field type, we determine the nature of the SIS type of epidemic phase transition in any network: the steady-state fraction of infected nodes y∞ is linear in (τfor effective infection rates τ ↓ τc, the derivative of y∞ at the epidemic threshold τc = 1 λ 1 is exactly computed and depends on the largest eigenvalue λ1 of the adjacency matrix and on the first-and third-order moments of the corresponding eigenvector. Since coupled oscillators in a network synchonize at a coupling strength proportional to,a similar characterization of the phase transition is suggested. The behavior of y∞ around τc was the missing part in the general steady-state theory of a SIS-type epidemic on a network.

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“…The more irregular a graph is, the smaller the slope, which agrees with simulations in [14]. Further, the inequality shows that slope decreases at least as fast as τ c = 1 λ1…”

Section: -P3supporting

confidence: 85%

Section: -P3mentioning

confidence: 97%

Epidemic phase transition of the SIS type in networks

Mieghem

2012

EPL

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“…If the effective spreading rate τ = β δ > τ c , the virus persists and a nonzero fraction of the nodes are infected, whereas for τ τ c , the epidemic dies out and the network is virus free in the steady state. From the point of view of network protection against viral infections, the epidemic threshold τ c is the key parameter in the design of immunization strategies in networks [8][9][10]. Many approximate methods applied to the SIS model have proposed various types of estimates for τ c .…”

Section: Introductionmentioning

confidence: 99%

Epidemics in networks with nodal self-infection and the epidemic threshold

Mieghem

Cator²

2012

Phys. Rev. E

125

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Since the Susceptible-Infected-Susceptible (SIS) epidemic threshold is not precisely defined in spite of its practical importance, the classical SIS epidemic process has been generalized to the ε−SIS model, where a node possesses a self-infection rate ε, in addition to a link infection rate β and a curing rate δ. The exact Markov equations are derived, from which the steady state can be computed. The major advantage of the ε−SIS model is that its steady state is different from the absorbing (or overall-healthy state) and approximates, for a certain range of small ε > 0, the in reality observed phase transition, also called the "metastable" state, that is characterized by the epidemic threshold. The exact steady-state analysis for the complete graph illustrates the effect of small ε and the quality of the first-order mean-field approximation, the N -intertwined model, proposed earlier. Apart from duality principles, often used in the mathematical literature, we present an exact recursion relation for the Markov infinitesimal generator.

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“…The last structural metric is viral conductance (VC), where the robustness is measured with respect to virus spread [20]. This metric is measured by considering the area under the curve that provides the fraction of infected nodes in steady-state for a range of epidemic intensities.…”

Section: Structural Metricsmentioning

confidence: 99%

Robustness Comparison of 15 Real Telecommunication Networks: Structural and Centrality Measurements

2016

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Multiple failures can have catastrophic consequences on the normal operation of telecommunication networks. In this sense, guaranteeing network robustness to avoid users and services being disconnected is essential. A wide range of metrics have been proposed for measuring network robustness. In this paper the taxonomy of robustness metrics in telecommunication networks has been extended and a classification of multiple failures scenarios has been made. Moreover, a structural and centrality robustness comparison of 15 real telecommunication networks experiencing multiple failures was carried out. Through this analysis the topological properties which are common for grouping networks with similar robustness are able to be identified.

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Viral conductance: Quantifying the robustness of networks with respect to spread of epidemics

Cited by 37 publications

References 29 publications

Epidemic phase transition of the SIS type in networks

Epidemic phase transition of the SIS type in networks

Epidemics in networks with nodal self-infection and the epidemic threshold

Robustness Comparison of 15 Real Telecommunication Networks: Structural and Centrality Measurements

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