Abstract
In a recent paper [Anwar Zeb, Gul Zaman, Shaher Momani, Square-root Dynamics of a Giving Up Smoking Model, Appl. Math. Model., 37 (2013) 5326-5334], the authors presented a new model of giving up smoking model. In this paper, we introduce three control variables in the form of education campaign, anti-smoking gum, and anti-nicotive drugs/medicine for the eradication of smoking in a community. Using the optimal control theory, the optimal levels of the three controls are characterized, and then the existence and uniqueness for the optimal control pair are established. In order to do this, we minimize the number of potential and occasional smokers and maximize the number of quit smokers. We use Pontryagin's maximum principle to characterize the optimal levels of the three controls. The resulting optimality system is solved numerically by Matlab.
Highlights
Modelling is a science which needs creative ability linked to a deep knowledge of the whole variety of methods offered by applied mathematics
Model., 37 (2013) 5326-5334], the authors presented a new model of giving up smoking model
The incidence of lung cancer is ten times greater in smokers than non-smokers and one out of ten people will die from this disease [1, 2, 3]
Summary
Modelling is a science which needs creative ability linked to a deep knowledge of the whole variety of methods offered by applied mathematics. Castillo-Garsow et al [1] proposed a simple mathematical model for giving up smoking They consider a system with total constant population which is divided into three classes: potential smokers (P), smokers (S), and quit smokers (Q). Sharomi and Gumel [2] developed the above model by introducing mild and chain classes They presented the development and public health impact of smoking related illnesses. Μ is natural death rate, γ is recover rate from infection, β is transmission coefficient, δ is quit rate of smoking, d represent death rate for potential smokers, occasional smoker, smoker and quit smoker related to smoking disease Beside this optimal control theory is another area of mathematics that is used extensively in controlling the spread of infectious diseases. Parameters estimation and numerical results are discussed in Section 4: we give conclusion
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