Percolation and Epidemics in a Two-Dimensional Small World
AbstractPercolation 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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Bibliographic InfoPaper provided by Santa Fe Institute in its series Working Papers with number 01-09-046.
Date of creation: Sep 2001
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Epidemics; networks; small world; series expansion;
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