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Computational and Mathematical Methods in Medicine
Volume 2014 (2014), Article ID 831506, 19 pages
http://dx.doi.org/10.1155/2014/831506
Research Article

Optimal Control of HIV/AIDS in the Workplace in the Presence of Careless Individuals

1Applied Mathematics Department, Faculty of Mathematical Sciences, University for Development, Navrongo, Ghana
2Faculty of Military Science, Stellenbosch University, Private Bag X2, Saldanha 7395, South Africa

Received 17 April 2014; Revised 29 May 2014; Accepted 31 May 2014; Published 26 June 2014

Academic Editor: Chung-Min Liao

Copyright © 2014 Baba Seidu and Oluwole D. Makinde. 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.

Abstract

A nonlinear dynamical system is proposed and qualitatively analyzed to study the dynamics of HIV/AIDS in the workplace. The disease-free equilibrium point of the model is shown to be locally asymptotically stable if the basic reproductive number, , is less than unity and the model is shown to exhibit a unique endemic equilibrium when the basic reproductive number is greater than unity. It is shown that, in the absence of recruitment of infectives, the disease is eradicated when , whiles the disease is shown to persist in the presence of recruitment of infected persons. The basic model is extended to include control efforts aimed at reducing infection, irresponsibility, and nonproductivity at the workplace. This leads to an optimal control problem which is qualitatively analyzed using Pontryagin’s Maximum Principle (PMP). Numerical simulation of the resulting optimal control problem is carried out to gain quantitative insights into the implications of the model. The simulation reveals that a multifaceted approach to the fight against the disease is more effective than single control strategies.