Optimal control strategies in square root dynamics of smoking model

  • Authors

    • Anwar Zeb Department of Mathematics COMSATS University Abbottabad, Pakistan
    • Fiza Bibi
    • Gul Zaman
    2015-03-10
    https://doi.org/10.14419/ijsw.v3i1.4138
  • Mathematical model, Square root dynamics, Non-standard, Finite difference scheme, Numerical analysis, Optimal control.

  • 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.

    Author Biography

    • Anwar Zeb, Department of Mathematics COMSATS University Abbottabad, Pakistan
      Epidemic models, Fuzzy algebra,Fractional Order Epidemicmodels, Controls in Epidemic models

  • References

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    Zeb, A., Bibi, F., & Zaman, G. (2015). Optimal control strategies in square root dynamics of smoking model. International Journal of Scientific World, 3(1), 91-97. https://doi.org/10.14419/ijsw.v3i1.4138