  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.
