2001/08/31 by M. E. J. Newman, Iwan Jensen, I. Jensen +2 · 2 citations
Biochemistry, Genetics and Molecular Biology · Medicine · Physics and Astronomy · #Complex Network Analysis Techniques #Mathematical and Theoretical Epidemiology and Ecology Models #Opinion Dynamics and Social Influence #cond-mat.dis-nn #cond-mat.stat-mech #q-bio
paper · pdf · doi:10.1103/physreve.65.021904
published as Phys. Rev. E 65, 021904 (2002) · 7 pages, 3 figures, 2 tables
arxiv created 2001/08/31 · openalex publication_date 2002/01/16 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.