Percolation and epidemics in a two-dimensional small world.
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.
Newman
M E J
ME
Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, New Mexico 87501, USA.
Jensen
I
I
Ziff
R M
RM
D055592:Biophysical Phenomena; D001703:Biophysics; D004196:Disease Outbreaks; D008954:Models, Biological; D015233:Models, Statistical; D010935:Plant Diseases