Percolation and Epidemics in a Two-Dimensional Small World

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

Working Papers from Santa Fe Institute

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.

Keywords: Epidemics; networks; small world; series expansion (search for similar items in EconPapers)
Date: 2001-09
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Persistent link: https://EconPapers.repec.org/RePEc:wop:safiwp:01-09-046

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