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Extinction times in multitype Markov branching processes


Heinzmann, D (2009). Extinction times in multitype Markov branching processes. Journal of Applied Probability, 46(1):296-307.

Abstract

In this paper, a distributional approximation to the time to extinction in a subcritical continuous-time Markov branching process is derived. A limit theorem for this distribution is established and the error in the approximation is quantified. The accuracy of the approximation is illustrated in an epidemiological example. Since Markov branching processes serve as approximations to nonlinear epidemic processes in the initial and final stages, our results can also be used to describe the time to extinction for such processes.

Abstract

In this paper, a distributional approximation to the time to extinction in a subcritical continuous-time Markov branching process is derived. A limit theorem for this distribution is established and the error in the approximation is quantified. The accuracy of the approximation is illustrated in an epidemiological example. Since Markov branching processes serve as approximations to nonlinear epidemic processes in the initial and final stages, our results can also be used to describe the time to extinction for such processes.

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6 citations in Web of Science®
5 citations in Scopus®
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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:2009
Deposited On:06 Nov 2009 07:18
Last Modified:05 Apr 2016 13:31
Publisher:Applied Probability Trust
ISSN:0021-9002
Publisher DOI:https://doi.org/10.1239/jap/1238592131
Official URL:http://projecteuclid.org/euclid.jap/1238592131
Related URLs:http://www.ams.org/mathscinet-getitem?mr=2508520

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