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Chaos in a spatial epidemic model

Publication ,  Journal Article
Durrett, R; Remenik, D
Published in: Annals of Applied Probability
August 1, 2009

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.

Duke Scholars

Published In

Annals of Applied Probability

DOI

EISSN

1050-5164

ISSN

1050-5164

Publication Date

August 1, 2009

Volume

19

Issue

4

Start / End Page

1656 / 1685

Related Subject Headings

  • Statistics & Probability
  • 0104 Statistics
  • 0102 Applied Mathematics
 

Citation

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MLA
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Durrett, R., & Remenik, D. (2009). Chaos in a spatial epidemic model. Annals of Applied Probability, 19(4), 1656–1685. https://doi.org/10.1214/08-AAP581
Durrett, R., and D. Remenik. “Chaos in a spatial epidemic model.” Annals of Applied Probability 19, no. 4 (August 1, 2009): 1656–85. https://doi.org/10.1214/08-AAP581.
Durrett R, Remenik D. Chaos in a spatial epidemic model. Annals of Applied Probability. 2009 Aug 1;19(4):1656–85.
Durrett, R., and D. Remenik. “Chaos in a spatial epidemic model.” Annals of Applied Probability, vol. 19, no. 4, Aug. 2009, pp. 1656–85. Scopus, doi:10.1214/08-AAP581.
Durrett R, Remenik D. Chaos in a spatial epidemic model. Annals of Applied Probability. 2009 Aug 1;19(4):1656–1685.

Published In

Annals of Applied Probability

DOI

EISSN

1050-5164

ISSN

1050-5164

Publication Date

August 1, 2009

Volume

19

Issue

4

Start / End Page

1656 / 1685

Related Subject Headings

  • Statistics & Probability
  • 0104 Statistics
  • 0102 Applied Mathematics