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
APA
Chicago
ICMJE
MLA
NLM
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