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Percolation and Epidemics in a Two-Dimensional Small World

Author

Listed:
  • M. E. J. Newman
  • I. Jensen
  • R. M. Ziff

Abstract

Percolation on two-dimensional small-world networks has been proposed as a model for the spread of plant diseases. In this paper we give an analytic solution of this model using a combination of generating function methods and high-order series expansion. Our solution gives accurate predictions for quantities such as the position of the percolation threshhold and the typical size of disease outbreaks as a function of the density of "shortcuts" in the small-world network. Our results agree with scaling hypotheses and numerical simulations for the same model.

Suggested Citation

  • M. E. J. Newman & I. Jensen & R. M. Ziff, 2001. "Percolation and Epidemics in a Two-Dimensional Small World," Working Papers 01-09-046, Santa Fe Institute.
    • Handle: RePEc:wop:safiwp:01-09-046
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    Keywords

    Epidemics; networks; small world; series expansion;
    All these keywords.

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