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The authors set up a time-continuous version of the first-order difference equation model of cocaine use introduced by Everingham and Rydell (MR-332-ONDCP/A/DPRC), and extend it by making initiation an endogenous function of prevalence. This function reflects both the epidemic spread of drug use as users "infect" non-users and the hypothesis that drug epidemics die out when a new generation is deterred from initiation by observing ill effects among heavy users. Their analysis suggests that drug prevention can temper drug prevalence and consumption, but that the effectiveness of drug treatment depends critically on the stage in the epidemic in which it is employed. Reducing the numbers of heavy users in the early stages can be counterproductive if it masks the risks of drug use and thereby removes a disincentive to initiation. The strong dependence of an intervention's effectiveness on the state of the dynamic system illustrates the pitfalls of applying a static control policy in a dynamic context.

Originally published in: Mathematical Biosciences, v. 159, 1999, pp. 1-20.

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