Abstract
During the last quarter of a century, dynamic models with multiple steady states have been studied in numerous areas of economics. The corresponding history-dependence of optimal paths constitutes a low-level form of complexity. The purpose of the present paper is to illustrate this fact for three selected models in the control of illicit drug consumption, which are validated with empirical data. In the first model, the dynamics of the current U.S. cocaine epidemic subject to law enforcement and treatment is studied. The second part augments the first model by taking into account the fact that enforcement activities influence not only the drug dynamics but also property crime. The third model investigates the influence of methadone maintenance treatment on the spread of HIV/HCV among injection drug users. In all three cases, a positive feedback effect, i.e. state-dependent initiation, is responsible for the occurrence of ‘Skiba points’ separating the basins of attraction of the multiple steady states.
This research was partly financed by the Austrian National Bank (ÖNB) under grant No.9414. We thank Maria Dworak and Julia Balta for providing files from their Master thesesthat were necessary to produce Sections 3 and 4, respectively. Finally, we thank Christian Almeder for revision of a preliminary version of this paper.
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Feichtinger, G., Tragler, G. (2002). Skiba Thresholds in Optimal Control of Illicit Drug Use. In: Zaccour, G. (eds) Optimal Control and Differential Games. Advances in Computational Management Science, vol 5. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-1047-5_1
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DOI: https://doi.org/10.1007/978-1-4615-1047-5_1
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