We investigate an interacting particle system inspired by the gypsy moth, whose populations grow until they become sufficiently dense so that an epidemic reduces them to a low level. We consider this process on a random 3-regular graph and on the d-dimensional lattice and torus, with d≥2. On the finite graphs with global dispersal or with a dispersal radius that grows with the number of sites, we prove convergence to a dynamical system that is chaotic for some parameter values. We conjecture that on the infinite lattice with a fixed finite dispersal distance, distant parts of the lattice oscillate out of phase so there is a unique nontrivial stationary distribution.
@article{1248700631,
author = {Durrett, Rick and Remenik, Daniel},
title = {Chaos in a spatial epidemic model},
journal = {Ann. Appl. Probab.},
volume = {19},
number = {1},
year = {2009},
pages = { 1656-1685},
language = {en},
url = {http://dml.mathdoc.fr/item/1248700631}
}
Durrett, Rick; Remenik, Daniel. Chaos in a spatial epidemic model. Ann. Appl. Probab., Tome 19 (2009) no. 1, pp. 1656-1685. http://gdmltest.u-ga.fr/item/1248700631/