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Ultimate Size of the Drug Addict Population
Author(s) -
Dayananda P. W. A.
Publication year - 1988
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.4710300215
Subject(s) - drug addict , population , mathematics , addiction , expression (computer science) , statistics , population size , distribution (mathematics) , statistical physics , econometrics , demography , psychology , computer science , mathematical analysis , physics , psychiatry , sociology , programming language
A model presented in a previous paper by Billard et al. (1985) on the spread of drug addiction in a closed population is further examined as a random walk process. The addiction process depends on the initial conditions and the parameters of the process. This paper considers the ultimate size of the drug addict population which is shown to satisfy a recurrence relation. A general expression for the distribution of the ultimate size of the number of drug addicts is derived; its expected size also presented. For given initial conditions and the values of the parameters, numerical values of the expected size of the ultimate number of addict population are presented and they are compared with the corresponding values for the deterministic model.