Percolation and epidemics in a two-dimensional small world

Details Percolation and epidemics in a two-dimensional small world Percolation and epidemics in a two-dimensional small world

2001-08-31

arxiv.org/abs/cond-mat/0108542v1

Phys. Rev. E 65, 021904 (2002)

Physics

Condensed Matter

Statistical Mechanics

7 pages, 3 figures, 2 tables

Scientific paper

10.1103/PhysRevE.65.021904

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.

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