Two-dimensional SIR epidemics with long range infection

Understand

We extend a recent study of susceptible-infected-removed epidemic processes with long range infection (referred to as I in the following) from 1-dimensional lattices to lattices in two dimensions.

• As in I we use hashing to simulate very large lattices for which finite size effects can be neglected, in spite of the assumed power law $p({\bf x})\sim |{\bf x}|^{-\sigma-2}$ for the probability that a site can infect another site a distance vector ${\bf x}$ apart.
• As in I we present detailed results for the critical case, for the supercritical case with $\sigma = 2$, and for the supercritical case with $0< \sigma < 2$.
• For the latter we verify the stretched exponential growth of the infected cluster with time predicted by M.