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The spatial general epidemic and locally dependent random graphs

Published online by Cambridge University Press:  14 July 2016

Kari Kuulasmaa
Kari Kuulasmaa*
Affiliation:
Heriot-Watt University
*
∗ Present address: Department of Applied Mathematics and Statistics, University of Oulu, SF-90570, Oulu 57, Finland.
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Abstract

The threshold behaviour of the stochastic spatial general epidemic model on a discrete location space is investigated by making use of the general percolation theory of McDiarmid.

Keywords

PERCOLATION PROCESSSPATIAL CONTACT PROCESSSPREAD OF EPIDEMIC
Type
Research Papers
Information
Journal of Applied Probability , Volume 19 , Issue 4 , December 1982 , pp. 745 - 758
Copyright
Copyright © Applied Probability Trust 1982 

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Footnotes

The research was supported by a Heriot-Watt University scholarship.

References

Dean, P. and Bird, N. F. (1967) Monte Carlo estimates for critical percolation probabilities. Proc. Camb. Phil. Soc. 63, 477–479.Google Scholar
Frisch, H. L. and Hammersley, J. M. (1963) Percolation processes and related topics. J. SIAM 11, 894–918.Google Scholar
Frisch, H. L., Sonnenblick, E., Vyssotsky, V. A. and Hammersley, J. M. (1961) Critical percolation probabilities (site problem). Phys. Rev. 124, 1021–1022.CrossRefGoogle Scholar
Hammersely, 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
Hammersley, J. M. and Handscomb, D. C. (1964) Monte Carlo Methods. Methuen, London.Google Scholar
Kesten, H. (1980) The critical probability of bond percolation on the square lattice equals . Commun. Math. Phys. 74, 41–59.Google Scholar
Kingman, J. F. C. (1978) Uses of exchangeability. Ann. Prob. 6, 183–197.Google Scholar
Mcdiarmid, C. (1981) General percolation and random graphs. Adv. Appl. Prob. 13, 40–60.CrossRefGoogle 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
Rota, G.-C. (1964) On the foundations of combinatorial theory 1; theory of Mobius functions. Z. Wahrscheinlichkeitsth. 2, 340–368.Google Scholar
Smythe, R. T. and Wierman, J. C. (1978) First Passage Percolation on the Square Lattice. Lecture Notes in Mathematics 671, Springer-Verlag, Berlin.CrossRefGoogle Scholar
Welsh, D. J. A. (1977) Percolation and related topics. Science Progress 64, 65–83.Google Scholar