English

Percolation and epidemics in a two-dimensional small world

Statistical Mechanics 2009-11-07 v1 Disordered Systems and Neural Networks q-bio

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

Cite

@article{arxiv.cond-mat/0108542,
  title  = {Percolation and epidemics in a two-dimensional small world},
  author = {M. E. J. Newman and I. Jensen and R. M. Ziff},
  journal= {arXiv preprint arXiv:cond-mat/0108542},
  year   = {2009}
}

Comments

7 pages, 3 figures, 2 tables

R2 v1 2026-07-22T10:26:54.989Z