Percolation and epidemics in a two-dimensional small world
- 16 January 2002
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review E
- Vol. 65 (2), 021904
- https://doi.org/10.1103/physreve.65.021904
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.Keywords
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