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Epidemics and Percolation in Small-World Networks

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  • Cristopher Moore
  • M. E. J. Newman
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    Abstract

    We study some simple models of disease transmission on small-world networks, in which either the probability of infection by a disease or the probability of its transmission is varied, or both. The resulting models display epidemic behavior when the infection or transmission probability rises above the threshold for site or bond percolation on the network, and we give exact solutions for the position of this threshold in a variety of cases. We confirm our analytic results by numerical simulation.

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    Bibliographic Info

    Paper provided by Santa Fe Institute in its series Working Papers with number 00-01-002.

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    Date of creation: Jan 2000
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    Handle: RePEc:wop:safiwp:00-01-002

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    Related research

    Keywords: Small world; disease spreading; epidemics; social networks; percolation.;

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    Cited by:
    1. Dassisti, M. & Carnimeo, L., 2013. "A small-world methodology of analysis of interchange energy-networks: The European behaviour in the economical crisis," Energy Policy, Elsevier, vol. 63(C), pages 887-899.
    2. Ball, Frank & Neal, Peter, 2003. "The great circle epidemic model," Stochastic Processes and their Applications, Elsevier, vol. 107(2), pages 233-268, October.
    3. Yang, Yang & Sun, Peng Gang & Hu, Xia & Li, Zhou Jun, 2014. "Closed walks for community detection," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 397(C), pages 129-143.
    4. Ganjeh-Ghazvini, Mostafa & Masihi, Mohsen & Ghaedi, Mojtaba, 2014. "Random walk–percolation-based modeling of two-phase flow in porous media: Breakthrough time and net to gross ratio estimation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 406(C), pages 214-221.
    5. Hsing Kenneth Cheng & Hong Guo, 2008. "Computer Virus Propagation in a Network Organization: The Interplay between Social and Technological Networks," Working Papers 08-24, NET Institute, revised Oct 2008.
    6. Paolo Zeppini & Koen Frenken & Luis R. Izquierdo, 2013. "Innovation diffusion in networks: the microeconomics of percolation," Eindhoven Center for Innovation Studies (ECIS) working paper series 13-02, Eindhoven Center for Innovation Studies (ECIS), revised Feb 2013.
    7. Cristopher Moore & M. E. J. Newman, 2000. "Exact Solution of Site and Bond Percolation on Small-World Networks," Working Papers 00-01-007, Santa Fe Institute.
    8. Foti, Nicholas J. & Pauls, Scott & Rockmore, Daniel N., 2013. "Stability of the World Trade Web over time – An extinction analysis," Journal of Economic Dynamics and Control, Elsevier, vol. 37(9), pages 1889-1910.
    9. Pan, Ya-Nan & Lou, Jing-Jing & Han, Xiao-Pu, 2014. "Outbreak patterns of the novel avian influenza (H7N9)," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 401(C), pages 265-270.
    10. Silva, S.L. & Ferreira, J.A. & Martins, M.L., 2007. "Epidemic spreading in a scale-free network of regular lattices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 377(2), pages 689-697.
    11. Andrea Giovannetti, 2012. "Financial Contagion in Industrial Clusters: A Dynamical Analysis and Network Simulation," Department of Economics University of Siena 654, Department of Economics, University of Siena.
    12. Sadeghnejad, S. & Masihi, M. & King, P.R., 2013. "Dependency of percolation critical exponents on the exponent of power law size distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(24), pages 6189-6197.
    13. Yang, Jianmei & Zhuang, Dong & Xie, Weicong & Chen, Guangrong, 2013. "A study of design approach of spreading schemes for viral marketing based on human dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(24), pages 6494-6505.
    14. M. E. J. Newman, 2001. "Clustering and Preferential Attachment in Growing Networks," Working Papers 01-03-021, Santa Fe Institute.

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