TY - JOUR
T1 - Percolation and epidemics in a two-dimensional small world
AU - Newman, M. E.J.
AU - Jensen, I.
AU - Ziff, R. M.
PY - 2002/2
Y1 - 2002/2
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=84872123888&partnerID=8YFLogxK
U2 - 10.1103/PhysRevE.65.021904
DO - 10.1103/PhysRevE.65.021904
M3 - Article
C2 - 11863560
AN - SCOPUS:84872123888
SN - 1063-651X
VL - 65
JO - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
JF - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
IS - 2
ER -