Optimal Control of Drug Epidemics: Prevent and Treat---But Not at the Same Time?

Doris A. Behrens (), Jonathan P. Caulkins (), Gernot Tragler () and Gustav Feichtinger
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Doris A. Behrens: Vienna University of Technology, Department of Operations Research and Systems Theory, Vienna, Austria, and Klagenfurt University, Department of Economics, Universitatssr. 65-67, A-9020 Klagenfurt, Austria
Jonathan P. Caulkins: H. John Heinz III School of Public Policy and Management, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213-3890, and RAND, Drug Policy Research Center, Santa Monica, California
Gernot Tragler: Vienna University of Technology, Department of Operations Research and Systems Theory, Vienna, Austria

Management Science, 2000, vol. 46, issue 3, 333-347

Abstract: Drug use and related problems change substantially over time, so it seems plausible that drug interventions should vary too. To investigate this possibility, we 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. We 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.

Keywords: illicit drug use; demand control; nonlinear dynamic Systems; Hopf-bifurcations; optimal control; public policy (search for similar items in EconPapers)
Date: 2000
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Citations: View citations in EconPapers (21)

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