Computational and Mathematical Methods in Medicine
Volume 2011 (2011), Article ID 163834, 9 pages
doi:10.1155/2011/163834
Research Article

Optimal Campaign in the Smoking Dynamics

Centre for Advanced Mathematics and Physics, National University of Sciences and Technology, H-12, Islamabad 64000, Pakistan

Received 16 June 2010; Accepted 16 December 2010

Academic Editor: Sivabal Sivaloganathan

Copyright © 2011 Gul Zaman. 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

We present the optimal campaigns in the smoking dynamics. Assuming that the giving up smoking model is described by the simplified 𝑃 𝐿 𝑆 𝑄 (potential-light-smoker-quit smoker) model, we consider two possible control variables in the form of education and treatment campaigns oriented to decrease the attitude towards smoking. In order to do this we minimize the number of light (occasional) and persistent smokers and maximize the number of quit smokers in a community. We first show the existence of an optimal control for the control problem and then derive the optimality system by using the Pontryagin maximum principle. Finally numerical results of real epidemic are presented to show the applicability and efficiency of this approach.