Journal
PHYSICAL REVIEW E
Volume 65, Issue 2, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevE.65.021904
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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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