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Journal of Applied Mathematics
Volume 2014, Article ID 104819, 17 pages
Research Article

HSV-2 and Substance Abuse amongst Adolescents: Insights through Mathematical Modelling

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

Received 5 July 2014; Accepted 5 October 2014; Published 13 November 2014

Academic Editor: Peter G. L. Leach

Copyright © 2014 A. Mhlanga et al. 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.


Herpes simplex virus infection is mostly spread and occurs more commonly among substance abusing adolescents as compared to the nonsubstance abusing. In this paper, a mathematical model for the spread of HSV-2 within a community with substance abusing adolescents is developed and analysed. The impacts of condom use and educational campaigns are examined. The study suggests that condom use is highly effective among adolescents, when we have more of them quitting than becoming substance abusers. Measures such as educational campaigns can be put in place to try and reduce adolescents from becoming substance abusers. Further, we applied optimal control theory to the proposed model. The controls represent condom use and educational campaigns. The objective is based on maximising the susceptible nonsubstance abusing adolescents, while minimising the susceptible substance abusing adolescents, the infectious nonsubstance abusing adolescents, and the infectious substance abusing adolescents. We used Pontrygin’s maximum principle to characterise the optimal levels of the two controls. The resulting optimality system is solved numerically. Overall, the application of the optimal control theory suggests that more effort should be devoted to condom use as compared to educational campaigns.