Percolation and Epidemics in a Two-Dimensional Small World
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.
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|Date of creation:||Sep 2001|
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Web page: http://www.santafe.edu/sfi/publications/working-papers.html
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