Abstract
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.
Citation
Rick Durrett. Daniel Remenik. "Chaos in a spatial epidemic model." Ann. Appl. Probab. 19 (4) 1656 - 1685, August 2009. https://doi.org/10.1214/08-AAP581
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