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Interparticle correlation in death processes with application to variability in compartmental models

Published online by Cambridge University Press:  01 July 2016

Frank Ball  and
Peter Donnelly
Frank Ball*
Affiliation:
University of Nottingham
Peter Donnelly*
Affiliation:
University College London
*
∗Postal address: Department of Mathematics, University of Nottingham, University Park, Nottingham NG7 2RD, UK.
∗∗Postal address: Department of Statistical Science, University College, Gower Street, London WC1E 6BT, UK.
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Abstract

This paper is concerned with a pure death process, starting with N individuals, with death rates μ n, n = 1, 2, …, N. It is shown that the fates of distinct individuals are positively correlated if μ n/n decreases with n, and negatively correlated if μ n/n increases with n. The application of this result to the problem of variability in compartmental models is elaborated and in particular a conjecture of Faddy (1985) is settled. Further applications to well-known death processes are also briefly described.

Keywords

CONCAVE AND CONVEX DEATH RATESFKG INEQUALITYDETERMINISTIC AND STOCHASTIC MODELSSIMPLE EPIDEMIC
Type
Research Article
Information
Advances in Applied Probability , Volume 19 , Issue 4 , December 1987 , pp. 755 - 766
Copyright
Copyright © Applied Probability Trust 1987 

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