UZH-Logo

Poisson approximation for some epidemic models


Ball, F; Barbour, A D (1990). Poisson approximation for some epidemic models. Journal of Applied Probability, 27(3):479-490.

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.

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.

Citations

Altmetrics

Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:1990
Deposited On:13 Apr 2010 12:06
Last Modified:05 Apr 2016 13:29
Publisher:Applied Probability Trust
ISSN:0021-9002
Publisher DOI:10.2307/3214534
Related URLs:http://www.jstor.org/stable/3214534
http://user.math.uzh.ch/barbour/pub/Barbour/BBall.pdf (Author)

Download

Full text not available from this repository.View at publisher

TrendTerms

TrendTerms displays relevant terms of the abstract of this publication and related documents on a map. The terms and their relations were extracted from ZORA using word statistics. Their timelines are taken from ZORA as well. The bubble size of a term is proportional to the number of documents where the term occurs. Red, orange, yellow and green colors are used for terms that occur in the current document; red indicates high interlinkedness of a term with other terms, orange, yellow and green decreasing interlinkedness. Blue is used for terms that have a relation with the terms in this document, but occur in other documents.
You can navigate and zoom the map. Mouse-hovering a term displays its timeline, clicking it yields the associated documents.

Author Collaborations