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Error bounds for deterministic approximations to Markov processes, with applications to epidemic models

Part of: Markov processes

Published online by Cambridge University Press:  14 July 2016

J. Gani  and
Sid Yakowitz
J. Gani*
Affiliation:
The Australian National University
Sid Yakowitz*
Affiliation:
University of Arizona
*
∗Postal address: Stochastic Analysis Group, School of Mathematical Sciences, The Australian National University, Canberra ACT 2000, Australia.
∗∗Postal address: Systems and Industrial Engineering Department, University of Arizona, Tucson, AZ 85721, USA.
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Abstract

The computer age and the phenomenological complexity of the AIDS/HIV epidemic have engendered a rich profusion of deterministic and stochastic time series models for the development of an epidemic. The present study examines the reliability of deterministic approximations of fundamentally random processes. Through numerical analysis and probabilistic considerations, we derive absolute and simultaneous confidence interval bounding techniques, and offer a practical procedure based on these developments. A heartening aspect of the computational study presented at the close of this paper indicates that when the population size is in the thousands, the deterministic version to the classical logistic epidemic is a good approximation.

Keywords

DYNAMIC POPULATION EPIDEMICSAIDSHIV

MSC classification

Primary: 92D30: Epidemiology
Secondary: 60J05: Discrete-time Markov processes on general state spaces
Type
Research Papers
Information
Journal of Applied Probability , Volume 32 , Issue 4 , December 1995 , pp. 1063 - 1076
Copyright
Copyright © Applied Probability Trust 1995 

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