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Control Strategies of Contagion Processes in Time-Varying Networks

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Temporal Network Epidemiology

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Abstract

The vast majority of strategies aimed at controlling contagion processes on networks consider a timescale separation between the evolution of the system and the unfolding of the process. However, in the real world, many networks are highly dynamical and evolve, in time, concurrently to the contagion phenomena. Here, we review the most commonly used immunization strategies on networks. In the first part of the chapter, we focus on controlling strategies in the limit of timescale separation. In the second part instead, we introduce results and methods that relax this approximation. In doing so, we summarize the main findings considering both numerical and analytically approaches in real as well as synthetic time-varying networks.

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Notes

  1. 1.

    The value of p and a c are linked by the relation \(p =\int _{ a_{c}}^{1}F(a)da\).

  2. 2.

    In order to guarantee that a fraction f of nodes is immunized the systems need to be observed for more than one time step. We define T ∗ as the average time needed for all the probes to have at least one interaction with other nodes. For any observation time T < T ∗ the fraction of immunized nodes will be in general p ≤ f.

  3. 3.

    As proposed by Lee et al. [86].

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Acknowledgements

The results presented in Sect. 8.3.2 are adapted from Ref. [84] and obtained in collaboration with S. Liu and A. Vespignani.

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Authors and Affiliations

  1. Univ de Lyon, ENS de Lyon, INRIA, CNRS, UMR 5668, IXXI, 69364, Lyon, France

    Márton Karsai

  2. Centre for Business Network Analysis, University of Greenwich, Park Row, London, SE10 9LS, UK

    Nicola Perra

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Correspondence to Márton Karsai .

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  1. Department of Engineering Mathematics, University of Bristol, Bristol, United Kingdom

    Naoki Masuda

  2. Institute of Innovative Research, Tokyo Institute of Technology, Yokohama, Japan

    Petter Holme

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Karsai, M., Perra, N. (2017). Control Strategies of Contagion Processes in Time-Varying Networks. In: Masuda, N., Holme, P. (eds) Temporal Network Epidemiology. Theoretical Biology. Springer, Singapore. https://doi.org/10.1007/978-981-10-5287-3_8

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