Finding a Better Immunization Strategy

Chen, Yiping; Paul, Gerald; Havlin, Shlomo; Liljeros, Fredrik; Stanley, H. Eugene

doi:10.1103/physrevlett.101.058701

Cited by 284 publications

(267 citation statements)

References 25 publications

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“…The robustness of a network is usually either characterized by the value of the critical threshold analysed using percolation theory 52 or defined as the integrated size of the largest connected cluster during the entire attack process 53 . The percolation approach was also proved to be extremely useful in addressing other scenarios, such as efficient attacks or immunization 6,7,54,55 , and for obtaining optimal paths 56 as well as for designing robust networks 53 . Network concepts have also proven to be useful for the analysis and understanding of the spread of epidemics 57,58 , and the organizational laws of social interactions, such as friendships 59,60 or scientific collaborations 61,62 .…”

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Networks formed from interdependent networks

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Complex networks appear in almost every aspect of science and technology. Although most results in the field have been obtained by analysing isolated networks, many real-world networks do in fact interact with and depend on other networks. The set of extensive results for the limiting case of non-interacting networks holds only to the extent that ignoring the presence of other networks can be justified. Recently, an analytical framework for studying the percolation properties of interacting networks has been developed. Here we review this framework and the results obtained so far for connectivity properties of 'networks of networks' formed by interdependent random networks.T he interdisciplinary field of network science has attracted a great deal of attention in recent years . This development is based on the enormous number of data that are now routinely being collected, modelled and analysed, concerning social 31-39 , economic 14,36,40,41 , technological 40,42-48 and biological 9,13,49,50 systems. The investigation and growing understanding of this extraordinary volume of data will enable us to make the infrastructures we use in everyday life more efficient and more robust.The original model of networks, random graph theory, was developed in the 1960s by ErdAEs and Rényi, and is based on the assumption that every pair of nodes is randomly connected with the same probability, leading to a Poisson degree distribution. In parallel, in physics, lattice networks, where each node has exactly the same number of links, have been studied to model physical systems. Although graph theory is a well-established tool in the mathematics and computer science literature, it cannot describe well modern, real-life networks. Indeed, the pioneering 1999 observation by Barabasi 2 , that many real networks do not follow the ErdAEs-Rényi model but that organizational principles naturally arise in most systems, led to an overwhelming accumulation of supporting data, new models and computational and analytical results, and to the emergence of a new science, that of complex networks.Complex networks are usually non-homogeneous structures that in many cases obey a power-law form in their degree (that is, number of links per node) distribution. These systems are called scale-free networks. Real networks that can be approximated as scale-free networks include the Internet 3 , the World Wide Web 4 , social networks 31-39 representing the relations between individuals, infrastructure networks such as those of airlines 51 , networks in biology 9,13,49,50 , in particular networks of proteinprotein interactions 10 , gene regulation and biochemical pathways, and networks in physics, such as polymer networks or the potentialenergy-landscape network. The discovery of scale-free networks led to a re-evaluation of the basic properties of networks, such as their robustness, which exhibit a drastically different character than those of ErdAEs-Rényi networks. For example, whereas homogeneous ErdAEs-Rényi networks are extremely vulnerable to random fa...

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Networks formed from interdependent networks

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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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“…In order to contain epidemics, several control measures were proposed that utilize network information. Epidemics can be suppressed by effective vaccination schemes such as the target vaccination [8], the acquaintance vaccination [9,10], the PageRank-based vaccination [11], and the graph partitioning vaccination [12]. Theoretically, the above vaccination schemes succeed in containing epidemics in which a network is highly heterogeneous although these vaccination schemes are considered as a preventive measure wherein it is necessary to complete vaccinations prior to the appearance of an infectious disease in a network.…”

Section: Introductionmentioning

confidence: 99%

Efficiency of prompt quarantine measures on a susceptible-infected-removed model in networks

Hasegawa

Nemoto

2017

Phys. Rev. E

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This study focuses on investigating the manner in which a prompt quarantine measure suppresses epidemics in networks. A simple and ideal quarantine measure is considered in which an individual is detected with a probability immediately after it becomes infected and the detected one and its neighbors are promptly isolated. The efficiency of this quarantine in suppressing a susceptible-infected-removed (SIR) model is tested in random graphs and uncorrelated scale-free networks. Monte Carlo simulations are used to show that the prompt quarantine measure outperforms random and acquaintance preventive vaccination schemes in terms of reducing the number of infected individuals. The epidemic threshold for the SIR model is analytically derived under the quarantine measure, and the theoretical findings indicate that prompt executions of quarantines are highly effective in containing epidemics. Even if infected individuals are detected with a very low probability, the SIR model under a prompt quarantine measure has finite epidemic thresholds in fat-tailed scale-free networks in which an infected individual can always cause an outbreak of a finite relative size without any measure. The numerical simulations also demonstrate that the present quarantine measure is effective in suppressing epidemics in real networks.

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Finding a Better Immunization Strategy

Cited by 284 publications

References 25 publications

Networks formed from interdependent networks

Networks formed from interdependent networks

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

Efficiency of prompt quarantine measures on a susceptible-infected-removed model in networks

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