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Related Experiment Videos

Percolation and epidemics in a two-dimensional small world.

M E J Newman1, I Jensen, R M Ziff

  • 1Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, New Mexico 87501, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 28, 2002
PubMed
Summary

This study models plant disease spread using percolation on small-world networks. An analytic solution accurately predicts disease outbreak size and percolation thresholds based on network shortcuts.

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Area of Science:

  • Complex systems
  • Network science
  • Epidemiology

Background:

  • Percolation theory models disease spread.
  • Small-world networks with shortcuts are relevant to real-world systems.

Purpose of the Study:

  • To develop an analytic solution for percolation on 2D small-world networks as a plant disease model.
  • To accurately predict percolation thresholds and disease outbreak sizes.

Main Methods:

  • Utilized generating function methods.
  • Employed high-order series expansion for analytic solution.

Main Results:

  • Achieved accurate predictions for percolation threshold position.
  • Quantified typical disease outbreak size relative to shortcut density.

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  • Results align with scaling hypotheses and numerical simulations.

    • Conclusions:

    • The analytic solution provides a robust framework for understanding disease spread on small-world networks.
    • This model accurately captures the impact of network topology on epidemic dynamics.