Optimal prevention and treatment in a dynamic drug model with diverse feedbacks and relapse / von Alexander Wasserburger
Weitere Titel
Optimale Prävention und Therapie in einem dynamischen Drogenmodell mit gemischtem Einfluss auf den Drogeneinstieg und der Möglichkeit von Rückfällen
VerfasserWasserburger, Alexander
Begutachter / BegutachterinTragler, Gernot
ErschienenWien 2016
Umfangvi, 71 Seiten : Diagramme
HochschulschriftTechnische Universität Wien, Univ., Diplomarbeit, 2016
Abweichender Titel nach Übersetzung der Verfasserin/des Verfassers
Schlagwörter (EN)Drugs / Optimal Control / Prevention / Treatment
URNurn:nbn:at:at-ubtuw:1-4677 Persistent Identifier (URN)
 Das Werk ist frei verfügbar
Optimal prevention and treatment in a dynamic drug model with diverse feedbacks and relapse [2.01 mb]
Zusammenfassung (Englisch)

This thesis aims at modelling and analysing the implications of potential relapse in a dynamic drug model. More precisely, an optimal control model incorporating the two states "drug users" and "teetotallers" is formulated. The main feature of the model is the fact that individuals quitting drug use do not simply leave the system but rather end up in the precarious state of a teetotaller with a certain risk of relapse. Relapsing teetotallers constitute a second inflow of drug users in addition to ordinary initiation. However, teetotallers are also assumed to have a dissuasive effect on initiation. Consequently, the number of teetotallers has both a positive and a negative effect on the overall drug problem. Moreover, the dynamical system is influenced by the controls "prevention" and "Treatment". Especially the use of treatment in consideration of high relapse rates is of substantial interest. After an introductory exploration of the underlying uncontrolled dynamics, Pontryagin's Maximum Principle is applied in order to solve the optimal control model. As a consequence of the model's complexity, the optimal solution and stable paths are calculated numerically using the Matlab-toolbox OCMat. Furthermore, a sensitivity analysis, describing the impact of variations of model parameters on the long-run solution, is conducted.