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The abundance threshold for plague as a critical percolation phenomenon

Author

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  • S. Davis

    (Theoretical Epidemiology, Faculty of Veterinary Medicine, University of Utrecht, Yalelaan 7, 3584 CL Utrecht, The Netherlands)

  • P. Trapman

    (Julius Center for Health Sciences and Primary Care, University Medical Center Utrecht, PO Box 85500, 3508 GA Utrecht, The Netherlands)

  • H. Leirs

    (University of Antwerp, Groenenborgerlaan 171, B-2020 Antwerp, Belgium
    Danish Pest Infestation Laboratory, University of Aarhus, Faculty of Agricultural Sciences, Skovbrynet 14, DK-2800 Kongens Lyngby, Denmark)

  • M. Begon

    (Host-Parasite Biology Research Group, School of Biological Sciences, University of Liverpool, Crown Street, Liverpool L69 7ZB, UK)

  • J. A. P. Heesterbeek

    (Theoretical Epidemiology, Faculty of Veterinary Medicine, University of Utrecht, Yalelaan 7, 3584 CL Utrecht, The Netherlands)

Abstract

Plague spread by numbers Percolation theory is a part of statistical physics that deals with the slow flow of liquid through porous media, and is more generally extended to consider the formation of long-range connectivity in a random system. It has been suggested that this theory might apply to the spread of infectious diseases in certain conditions, but no natural examples have been reported until now. A disease that does behave in this way is plague (Yersinia pestis infection) among great gerbils in Central Asia. The flea dispersal movements carrying plague from one family group of great gerbils to another are small compared to the vast areas of the desert habitat. This equates to a system in which plague percolates through an area only if the landscape is sufficiently filled with family groups of hosts.

Suggested Citation

  • S. Davis & P. Trapman & H. Leirs & M. Begon & J. A. P. Heesterbeek, 2008. "The abundance threshold for plague as a critical percolation phenomenon," Nature, Nature, vol. 454(7204), pages 634-637, July.
    • Handle: RePEc:nat:nature:v:454:y:2008:i:7204:d:10.1038_nature07053
    DOI: 10.1038/nature07053
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    Cited by:

    1. Patrick W. Schmidt, 2020. "Inference under Superspreading: Determinants of SARS-CoV-2 Transmission in Germany," Papers 2011.04002, arXiv.org.
    2. Paolo Zeppini & Koen Frenken & Luis R. Izquierdo, 2013. "Innovation diffusion in networks: the microeconomics of percolation," Working Papers 13-02, Eindhoven Center for Innovation Studies, revised Feb 2013.
    3. Alexander Veremyev & Oleg A. Prokopyev & Sergiy Butenko & Eduardo L. Pasiliao, 2016. "Exact MIP-based approaches for finding maximum quasi-cliques and dense subgraphs," Computational Optimization and Applications, Springer, vol. 64(1), pages 177-214, May.
    4. Laperrière, Vincent & Brugger, Katharina & Rubel, Franz, 2016. "Cross-scale modeling of a vector-borne disease, from the individual to the metapopulation: The seasonal dynamics of sylvatic plague in Kazakhstan," Ecological Modelling, Elsevier, vol. 342(C), pages 34-48.
    5. Sean M Moore & Andrew Monaghan & Kevin S Griffith & Titus Apangu & Paul S Mead & Rebecca J Eisen, 2012. "Improvement of Disease Prediction and Modeling through the Use of Meteorological Ensembles: Human Plague in Uganda," PLOS ONE, Public Library of Science, vol. 7(9), pages 1-11, September.
    6. Huang, Xudong & Yang, Dong & Kang, Zhiqin, 2021. "Impact of pore distribution characteristics on percolation threshold based on site percolation theory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 570(C).

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