Chaos in a spatial epidemic model

Published

Journal Article

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.

Full Text

Duke Authors

Cited Authors

  • Durrett, R; Remenik, D

Published Date

  • August 1, 2009

Published In

Volume / Issue

  • 19 / 4

Start / End Page

  • 1656 - 1685

Electronic International Standard Serial Number (EISSN)

  • 1050-5164

International Standard Serial Number (ISSN)

  • 1050-5164

Digital Object Identifier (DOI)

  • 10.1214/08-AAP581

Citation Source

  • Scopus