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A modification of the general stochastic epidemic motivated by AIDS modelling

Part of: Markov processes

Published online by Cambridge University Press:  01 July 2016

Frank Ball  and
Philip O'neill
Frank Ball*
Affiliation:
University of Nottingham
Philip O'neill
Affiliation:
University of Nottingham
*
∗Postal address: Department of Mathematics, University of Nottingham, University Park, Nottingham NG7 2RD, UK.
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Abstract

This paper considers a model for the spread of an epidemic in a closed, homogeneously mixing population in which new infections occur at rate βxy/(x + y), where x and y are the numbers of susceptible and infectious individuals, respectively, and β is an infection parameter. This contrasts with the standard general epidemic in which new infections occur at rate βxy. Both the deterministic and stochastic versions of the modified epidemic are analysed. The deterministic model is completely soluble. The time-dependent solution of the stochastic model is derived and the total size distribution is considered. Threshold theorems, analogous to those of Whittle (1955) and Williams (1971) for the general stochastic epidemic, are proved for the stochastic model. Comparisons are made between the modified and general epidemics. The effect of introducing variability in susceptibility into the modified epidemic is studied.

Keywords

EPIDEMICSSIZE OF EPIDEMICDETERMINISTIC AND STOCHASTIC MODELSTIME-DEPENDENT SOLUTIONTHRESHOLD THEOREMSEMBEDDED RANDOM WALKSVARIABILITY IN SUSCEPTIBILITY

MSC classification

Primary: 92D30: Epidemiology
Secondary: 60J27: Continuous-time Markov processes on discrete state spaces
Type
Research Article
Information
Advances in Applied Probability , Volume 25 , Issue 1 , March 1993 , pp. 39 - 62
Copyright
Copyright © Applied Probability Trust 1993 

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Footnotes

∗∗

Present address: Department of Mathematics, University of Bradford, Bradford BD7 1DP, UK.

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