Centre for Advanced Mathematics and Physics, National University of Sciences and Technology, H-12, Islamabad 64000, Pakistan
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.
We present the optimal campaigns in the smoking dynamics. Assuming
that the giving up smoking model is described by the simplified (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.