Optimal Control of Drug Epidemics

Prevent and Treat--But Not at the Same Time?

Published in: Management Science, v. 46, no. 3, Mar. 2000, p. 333-347

Posted on RAND.org on December 31, 1999

by Doris A. Behrens, Jonathan P. Caulkins, Gernot Tragler, Gustav Feichtinger

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Drug use and related problems change substantially over time, so it seems plausible that drug interventions should vary too. To investigate this possibility, the authors set up a continuous time version of the first-order difference equation model of cocaine use introduced by Everingham and Rydell (1994), extended to make initiation an endogenous function of prevalence. They then formulate and solve drug treatment and prevention spending decisions in the framework of dynamic optimal control under different assumptions about how freely drug control budgets can be manipulated. Insights include: (1) The effectiveness of prevention and treatment depend critically on the stage in the epidemic in which they are employed. Prevention is most appropriate when there are relatively few heavy users, e.g. in the beginning of an epidemic. Treatment is more effective later. (2) Hence, the optimal mix of interventions varies over time. (3) The transition period when it is optimal to use extensively both prevention and treatment is brief. (4) Total social costs increase dramatically if control is delayed.

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