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    Epidemic thresholds of the susceptible-infected-susceptible model on networks: A comparison of numerical and theoretical results

    Silvio C. Ferreira1, Claudio Castellano2,3, and Romualdo Pastor-Satorras4

    • 1Departamento de Física, Universidade Federal de Viçosa, 36571-000, Viçosa - MG, Brazil
    • 2Istituto dei Sistemi Complessi (ISC-CNR), via dei Taurini 19, I-00185 Roma, Italy
    • 3Dipartimento di Fisica, “Sapienza” Università di Roma, P.le A. Moro 2, I-00185 Roma, Italy
    • 4Departament de Física i Enginyeria Nuclear, Universitat Politècnica de Catalunya, Campus Nord B4, 08034 Barcelona, Spain

    Phys. Rev. E 86, 041125 – Published 15 October, 2012

    DOI: https://doi.org/10.1103/PhysRevE.86.041125

    Abstract

    Recent work has shown that different theoretical approaches to the dynamics of the susceptible-infected-susceptible (SIS) model for epidemics lead to qualitatively different estimates for the position of the epidemic threshold in networks. Here we present large-scale numerical simulations of the SIS dynamics on various types of networks, allowing the precise determination of the effective threshold for systems of finite size N. We compare quantitatively the numerical thresholds with theoretical predictions of the heterogeneous mean-field theory and of the quenched mean-field theory. We show that the latter is in general more accurate, scaling with N with the correct exponent, but often failing to capture the correct prefactor.

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