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Strong approximations for some open population epidemic models

Part of: Special processes

Published online by Cambridge University Press:  14 July 2016

Philip O'Neill
Philip O'Neill*
Affiliation:
University of Bradford
*
∗ Postal address: Department of Mathematics, University of Bradford, Bradford, BD7 1DP, UK.
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Abstract

This paper considers a class of epidemic models in which susceptibles may enter or leave the population according to a general continuous time density dependent Markov chain. A sequence of such epidemics indexed by N, the initial number of susceptibles, is constructed on the same probability space as a time-inhomogeneous birth-and-death process. A coupling argument is then used to demonstrate the strong convergence of the sequence of infectives to the birth-and-death process. This result is used to provide a threshold analysis of the epidemic model in question.

Keywords

EPIDEMICSSIZE OF EPIDEMICCOUPLING METHODSBIRTH-AND-DEATH PROCESSESDENSITYDEPENDENT MARKOV CHAINS

MSC classification

Primary: 92D30: Epidemiology
Secondary: 60K99: None of the above, but in this section

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 33 , Issue 2 , September 1996 , pp. 448 - 457
Copyright
Copyright © Applied Probability Trust 1996 

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