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Percolation and epidemics in a two-dimensional small world

M. E. J. Newman·I. Jensen·R. M. Ziff
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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 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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M. E. J. Newman, I. Jensen, R. M. Ziff. 2001-08-31. Percolation and epidemics in a two-dimensional small world. https://doi.org/10.1103/physreve.65.021904

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