The Annals of Applied Probability

Chaos in a spatial epidemic model

Rick Durrett and Daniel Remenik

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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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Ann. Appl. Probab. Volume 19, Number 4 (2009), 1656-1685.

First available in Project Euclid: 27 July 2009

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Zentralblatt MATH identifier

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 60J10: Markov chains (discrete-time Markov processes on discrete state spaces) 92D25: Population dynamics (general) 37D45: Strange attractors, chaotic dynamics 37N25: Dynamical systems in biology [See mainly 92-XX, but also 91-XX]

Epidemic model chaos interacting particle system dynamical system random graph gypsy moth


Durrett, Rick; Remenik, Daniel. Chaos in a spatial epidemic model. Ann. Appl. Probab. 19 (2009), no. 4, 1656--1685. doi:10.1214/08-AAP581.

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