Percolation and epidemics in a two-dimensional small world

M. E.J. Newman, I. Jensen, R. M. Ziff

Research output: Contribution to journalArticlepeer-review

113 Citations (Scopus)

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 threshold 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.

Original languageEnglish
Number of pages7
JournalPhysical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
Volume65
Issue number2
DOIs
Publication statusPublished - Feb 2002
Externally publishedYes

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