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A drug addiction model

Published online by Cambridge University Press:  14 July 2016

L. Billard  and
P. W. A. Dayananda
L. Billard*
Affiliation:
University of Georgia
P. W. A. Dayananda*
Affiliation:
University of Georgia
*
∗Postal address for both authors: Department of Statistics, The University of Georgia, Athens, GA 30602, USA.
∗Postal address for both authors: Department of Statistics, The University of Georgia, Athens, GA 30602, USA.
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Abstract

A drug addiction process in which individuals in a closed population can become addicts or pushers is modelled. Expressions for the state probabilities and factorial moments are obtained. A generalized model is also developed. This generalized drug addiction process can be viewed as a particular case of what may be called a competing death process.

Keywords

SUSCEPTIBLESADDICTSPUSHERSSTATE PROBABILITIESFACTORIAL MOMENTSCOMPETING DEATH PROCESS
Type
Research Papers
Information
Journal of Applied Probability , Volume 25 , Issue 4 , December 1988 , pp. 649 - 662
Copyright
Copyright © Applied Probability Trust 1988 

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Footnotes

†

Research partially supported by National Institute of Health Grant No. 5 RO1 GM 30325, and Office of Naval Research Grant No. N00014–87-K 0499.

∗

On leave from Griffith University.

References

Billard, L. (1973) Factorial moments and probabilities for the general stochastic epidemic. J. Appl. Prob. 10, 277–288.Google Scholar
Demarce, R. G., Hudiburg, R. A., and Fletcher, B. W. (1980) The estimates of prevalence of heroin use in 24 Metropolitan Areas and Nationwide, 1976–79, NIDA Research Project, U.S. Department of Health and Human Services.Google Scholar
Hughes, P. H., Senay, E. C. and Parker, R. (1972) The medical management of a heroin epidemic. Arch. Gen. Psychiat. 27, 585–591.Google Scholar
Kermack, W. O. and Mckendrick, A. G. (1927) Contributions to the mathematical theory of epidemics. Proc. R. Soc. A 115, 700–721.Google Scholar
Newmeyer, J. A. and Johnson, G. R. (1976) The heroin epidemic in San Francisco: Estimates of incidence and prevalence. Int. J. Addiction 11, 417–438.Google Scholar
Severo, N. C. (1969) A recursion theorem on solving differential-difference equations and applications to some stochastic processes. J. Appl. Prob. 6, 673–681.Google Scholar