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

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.

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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

Information

Published: August 2009
First available in Project Euclid: 27 July 2009

zbMATH: 1181.92072
MathSciNet: MR2538084
Digital Object Identifier: 10.1214/08-AAP581

Subjects:
Primary: 37D45 , 37N25 , 60J10 , 60K35 , 92D25

Keywords: chaos , dynamical system , Epidemic model , gypsy moth , Interacting particle system , random graph

Rights: Copyright © 2009 Institute of Mathematical Statistics

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Vol.19 • No. 4 • August 2009
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