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


  • 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)

  • Gustav Feichtinger

    () (Vienna University of Technology, Department of Operations Research and Systems Theory, Vienna, Austria)


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.

Suggested Citation

  • Doris A. Behrens & Jonathan P. Caulkins & Gernot Tragler & Gustav Feichtinger, 2000. "Optimal Control of Drug Epidemics: Prevent and Treat---But Not at the Same Time?," Management Science, INFORMS, vol. 46(3), pages 333-347, March.
  • Handle: RePEc:inm:ormnsc:v:46:y:2000:i:3:p:333-347

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    References listed on IDEAS

    1. Sohler Everingham, Susan M. & Peter Rydell, C. & Caulkins, Jonathan P., 1995. "Cocaine consumption in the United States: Estimating past trends and future scenarios," Socio-Economic Planning Sciences, Elsevier, vol. 29(4), pages 305-314, December.
    2. Frank M. Bass, 1969. "A New Product Growth for Model Consumer Durables," Management Science, INFORMS, vol. 15(5), pages 215-227, January.
    3. Gustav Feichtinger & Richard F. Hartl & Suresh P. Sethi, 1994. "Dynamic Optimal Control Models in Advertising: Recent Developments," Management Science, INFORMS, vol. 40(2), pages 195-226, February.
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    Cited by:

    1. Kaplan, Edward H., 2008. "Adventures in policy modeling! Operations research in the community and beyond," Omega, Elsevier, vol. 36(1), pages 1-9, February.
    2. Caulkins, Jonathan P. & Feichtinger, Gustav & Tragler, Gernot & Wallner, Dagmar, 2010. "When in a drug epidemic should the policy objective switch from use reduction to harm reduction?," European Journal of Operational Research, Elsevier, vol. 201(1), pages 308-318, February.
    3. Rowthorn, Robert & Toxvaerd, Flavio, 2012. "The Optimal Control of Infectious Diseases via Prevention and Treatment," CEPR Discussion Papers 8925, C.E.P.R. Discussion Papers.
    4. Zeiler, I. & Caulkins, J.P. & Tragler, G., 2011. "Optimal control of interacting systems with DNSS property: The case of illicit drug use," Journal of Economic Behavior & Organization, Elsevier, vol. 78(1), pages 60-73.
    5. I. Zeiler & J.P. Caulkins & G. Tragler, 2011. "Optimal Control of Interacting Systems with DNSS Property: The Case of Illicit Drug Use," Post-Print hal-00978258, HAL.
    6. Behrens, Doris A. & Caulkins, Jonathan P. & Tragler, Gernot & Feichtinger, Gustav, 2002. "Why present-oriented societies undergo cycles of drug epidemics," Journal of Economic Dynamics and Control, Elsevier, vol. 26(6), pages 919-936, June.
    7. Rossi, Carla, 2004. "Operational models for epidemics of problematic drug use: the Mover-Stayer approach to heterogeneity," Socio-Economic Planning Sciences, Elsevier, vol. 38(1), pages 73-90, March.
    8. Herbert Dawid & Engelbert Dockner & Richard Hartl & Josef Haunschmied & Ulrike Leopold-Wildburger & Mikulas Luptacik & Alexander Mehlmann & Alexia Prskawetz & Marion Rauner & Gerhard Sorger & Gernot T, 2010. "Gustav Feichtinger celebrates his 70th birthday," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 18(4), pages 437-451, December.
    9. Massin, Sophie, 2012. "Is harm reduction profitable? An analytical framework for corporate social responsibility based on an epidemic model of addictive consumption," Social Science & Medicine, Elsevier, vol. 74(12), pages 1856-1863.
    10. Seidl, Andrea & Kaplan, Edward H. & Caulkins, Jonathan P. & Wrzaczek, Stefan & Feichtinger, Gustav, 2016. "Optimal control of a terror queue," European Journal of Operational Research, Elsevier, vol. 248(1), pages 246-256.
    11. Konrad, Renata A. & Trapp, Andrew C. & Palmbach, Timothy M. & Blom, Jeffrey S., 2017. "Overcoming human trafficking via operations research and analytics: Opportunities for methods, models, and applications," European Journal of Operational Research, Elsevier, vol. 259(2), pages 733-745.
    12. Kaya, C. Yalcin, 2004. "Time-optimal switching control for the US cocaine epidemic," Socio-Economic Planning Sciences, Elsevier, vol. 38(1), pages 57-72, March.


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