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Poisson approximation for some epidemic models

Published online by Cambridge University Press:  14 July 2016

Frank Ball  and
A. D. Barbour
Frank Ball*
Affiliation:
University of Nottingham
A. D. Barbour*
Affiliation:
Universität Zurich
*
∗ Postal address: Department of Mathematics, University of Nottingham, University Park, Nottingham NG7 2RD, UK.
∗∗ Postal address: Institut für Angewandte Mathematik, Universität Zürich, Rämistrasse 74, CH-8001 Zürich, Switzerland.
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Abstract

The Daniels' Poisson limit theorem for the final size of a severe general stochastic epidemic is extended to the Martin-Löf epidemic, and an order of magnitude for the error in the approximation is also given. The argument consists largely of showing that the number of survivors of a severe epidemic is essentially the same as the number of isolated vertices in a random directed graph. Poisson approximation for the latter quantity is proved using the Stein–Chen method and a suitable coupling.

Keywords

STEIN–CHEN METHODEPIDEMIC SIZERANDOM GRAPH

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 27 , Issue 3 , September 1990 , pp. 479 - 490
Copyright
Copyright © Applied Probability Trust 1990 

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References

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