Article

Global efficiency of local immunization on complex networks

Département de Physique, de Génie Physique, et d'Optique, Université Laval, Québec (Québec), Canada G1V 0A6.
Scientific Reports (Impact Factor: 5.58). 07/2013; 3:2171. DOI: 10.1038/srep02171
Source: PubMed

ABSTRACT

Epidemics occur in all shapes and forms: infections propagating in our sparse sexual networks, rumours and diseases spreading through our much denser social interactions, or viruses circulating on the Internet. With the advent of large databases and efficient analysis algorithms, these processes can be better predicted and controlled. In this study, we use different characteristics of network organization to identify the influential spreaders in 17 empirical networks of diverse nature using 2 epidemic models. We find that a judicious choice of local measures, based either on the network's connectivity at a microscopic scale or on its community structure at a mesoscopic scale, compares favorably to global measures, such as betweenness centrality, in terms of efficiency, practicality and robustness. We also develop an analytical framework that highlights a transition in the characteristic scale of different epidemic regimes. This allows to decide which local measure should govern immunization in a given scenario.

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Available from: Laurent Hébert-Dufresne, Jun 02, 2014
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    • "Percolation on graphs offers a simple theoretical framework to model and investigate the behavior of many complex systems; noteworthy examples being the growth and the robustness of their structure [1] [2], their observability [3] [4], as well as the effect of their structure on the propagation of emerging infectious agents [5] [6]. On the analytical front, recent progress has been mainly achieved within the Configuration Model (CM) paradigm [7], which, in the limit of large graphs, allows an exact and simple analytical treatment with the use of probability generating functions (pgf) [8] [9]. "
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    ABSTRACT: We present a comprehensive and versatile theoretical framework to study site and bond percolation on clustered and correlated random graphs. Our contribution can be summarized in three main points. (i) We introduce a set of iterative equations that solve the exact distribution of the size and composition of components in finite size quenched or random multitype graphs. (ii) We define a very general random graph ensemble that encompasses most of the models published to this day, and also that permits to model structural properties not yet included in a theoretical framework. Site and bond percolation on this ensemble is solved exactly in the infinite size limit using probability generating functions [i.e., the percolation threshold, the size and the composition of the giant (extensive) and small components]. Several examples and applications are also provided. (iii) Our approach can be adapted to model interdependent graphs---whose most striking feature is the emergence of an extensive component via a discontinuous phase transition---in an equally general fashion. We show how a graph can successively undergo a continuous then a discontinuous phase transition, and preliminary results suggest that clustering increases the amplitude of the discontinuity at the transition.
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    • "We have not considered k-core centrality for evaluation as it is shown to be not very effective in finding the influential nodes for targeted immunization.[14] 1. global deg: Degree centrality denotes the number of immediate neighbors of a node, i.e. which are only one edge away from the node. "
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    ABSTRACT: Understanding the epidemic dynamics, and finding out efficient techniques to control it, is a challenging issue. A lot of research has been done on targeted immunization strategies, exploiting various global network topological properties. However, in practice, information about the global structure of the contact network may not be available. Therefore, immunization strategies that can deal with a limited knowledge of the network structure are required. In this paper, we propose targeted immunization strategies that require information only at the community level. Results of our investigations on the SIR epidemiological model, using a realistic synthetic benchmark with controlled community structure, show that the community structure plays an important role in the epidemic dynamics. An extensive comparative evaluation demonstrates that the proposed strategies are as efficient as the most influential global centrality based immunization strategies, despite the fact that they use a limited amount of information. Furthermore, they outperform alternative local strategies, which are agnostic about the network structure, and make decisions based on random walks.
    Full-text · Article · Nov 2014
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    • "Among many ingredients for quick and wide spreading, influential spreaders play a major role [5] [6] [7]. Accordingly, immunization on large-degree nodes (they are usually considered to be more influential) is a highly efficient method to control epidemic spreading [8] [9] [10]. It is of great theoretical and practical significance to identify influential spreaders in networks, and similar methods can be applied in ranking scientists [11] [12], publications [12], athletes [13] and finding influential directors [14]. "
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