Chaos in a spatial epidemic model
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. © Institute of Mathematical Statistics, 2009.
Volume / Issue
Start / End Page
Electronic International Standard Serial Number (EISSN)
International Standard Serial Number (ISSN)
Digital Object Identifier (DOI)