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On spàtial general epidemics and bond percolation processes

Published online by Cambridge University Press:  14 July 2016

Kari Kuulasmaa  and
Stan Zachary
Kari Kuulasmaa*
Affiliation:
University of Oulu
Stan Zachary*
Affiliation:
Heriot-Watt University
*
∗Present address: National Public Health Institute, Department of Epidemiology, Mannerheimintie 166, SF-00280 Helsinki, Finland.
∗∗Postal address: Department of Actuarial Mathematics and Statistics, Heriot-Watt University, Riccarton, Edinburgh EH14 4AS, UK.
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Abstract

We show that a lower bound for the probability that a spatial general epidemic never becomes extinct is given by the percolation probability of an associated bond percolation process.

Keywords

PERCOLATION PROCESS
Type
Short Communications
Information
Journal of Applied Probability , Volume 21 , Issue 4 , December 1984 , pp. 911 - 914
Copyright
Copyright © Applied Probability Trust 1984 

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References

Hammersley, J. M. (1957) Bornes supérieures de la probabilité critique dans un processus de filtration. In Le calcul des probabilités et ses applications, Proc. 87th International Colloquium CNRS, Paris, 17–37.Google Scholar
Kesten, H. (1980) The critical probability of bond percolation on the square lattice equals ½. Commun. Math. Phys. 74, 41–59.Google Scholar
Kuulasmaa, K. (1982) The spatial general epidemic and locally dependent random graphs. J. Appl. Prob. 19, 745–758.Google Scholar
Mcdiarmid, C. (1981) General percolation and random graphs. Adv. Appl. Prob. 13, 40–60.Google Scholar
Mollison, D. (1977) Spatial contact models for ecological and epidemic spread. J. R. Statist. Soc. B 39, 283–326.Google Scholar
Mollison, D. (1978) Markovian contact processes. Adv. Appl. Prob. 10, 85–108.Google Scholar
Wierman, J. C. (1981) Bond percolation on honeycomb and triangular lattices. Adv. Appl. Prob. 13, 298–313.Google Scholar