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Multivariate birth-and-death processes as approximations to epidemic processes

Published online by Cambridge University Press:  14 July 2016

D. A. Griffiths
D. A. Griffiths*
Affiliation:
University of Oxford
*
∗ Now at: C. S. I. R. O. 60 King Street, Newtown, N. S. W., Australia.
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Abstract

This paper presents the theory of a multivariate birth-and-death process and its representation as a branching process. The bivariate linear birth-and-death process may be used as a model for various epidemic situations involving two types of infective. Various properties of the transient process are discussed and the distribution of epidemic size is investigated. For the case of a disease spread solely by carriers when the two types of infective are carriers and clinical infectives the large population version of a model proposed by Downton (1968) is further developed and shown under appropriate circumstances to closely approximate Downton's model.

Keywords

CARRIER-BORNE EPIDEMICSMULTIVARIATE LINEAR BIRTH-AND-DEATH PROCESSLARGE POPULATION EPIDEMIC MODEL

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 10 , Issue 1 , March 1973, pp. 15 - 26
Copyright
Copyright © Applied Probability Trust 1973 

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