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Computational and Mathematical Methods in Medicine
Volume 2015, Article ID 383154, 11 pages
Research Article

Modeling Illicit Drug Use Dynamics and Its Optimal Control Analysis

University of Zimbabwe, Department of Mathematics, P.O. Box MP 167, Harare, Zimbabwe

Received 20 April 2015; Accepted 13 October 2015

Academic Editor: Seiya Imoto

Copyright © 2015 Steady Mushayabasa and Gift Tapedzesa. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The global burden of death and disability attributable to illicit drug use, remains a significant threat to public health for both developed and developing nations. This paper presents a new mathematical modeling framework to investigate the effects of illicit drug use in the community. In our model the transmission process is captured as a social “contact” process between the susceptible individuals and illicit drug users. We conduct both epidemic and endemic analysis, with a focus on the threshold dynamics characterized by the basic reproduction number. Using our model, we present illustrative numerical results with a case study in Cape Town, Gauteng, Mpumalanga and Durban communities of South Africa. In addition, the basic model is extended to incorporate time dependent intervention strategies.