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  • Open Access


    Optimal Control and Spectral Collocation Method for Solving Smoking Models

    Amr M. S. Mahdy1,*, Mohamed S. Mohamed1, Ahoud Y. Al Amiri2, Khaled A. Gepreel1

    Intelligent Automation & Soft Computing, Vol.31, No.2, pp. 899-915, 2022, DOI:10.32604/iasc.2022.017801

    Abstract In this manuscript, we solve the ordinary model of nonlinear smoking mathematically by using the second kind of shifted Chebyshev polynomials. The stability of the equilibrium point is calculated. The schematic of the model illustrates our proposition. We discuss the optimal control of this model, and formularize the optimal control smoking work through the necessary optimality cases. A numerical technique for the simulation of the control problem is adopted. Moreover, a numerical method is presented, and its stability analysis discussed. Numerical simulation then demonstrates our idea. Optimal control for the model is further discussed by clarifying the optimal control through… More >

  • Open Access


    A Structure Preserving Numerical Method for Solution of Stochastic Epidemic Model of Smoking Dynamics

    Ali Raza1, Muhammad Rafiq2, Nauman Ahmed3, Ilyas Khan4, *, Kottakkaran Sooppy Nisar5, Zafar Iqbal3

    CMC-Computers, Materials & Continua, Vol.65, No.1, pp. 263-278, 2020, DOI:10.32604/cmc.2020.011289

    Abstract In this manuscript, we consider a stochastic smoking epidemic model from behavioural sciences. Also, we develop a structure preserving numerical method to describe the dynamics of stochastic smoking epidemic model in a human population. The structural properties of a physical system include positivity, boundedness and dynamical consistency. These properties play a vital role in non-linear dynamics. The solution for nonlinear stochastic models necessitates the conservation of these properties. Unfortunately, the aforementioned properties of the model have not been restored in the existing stochastic methods. Therefore, it is essential to construct a structure preserving numerical method for a reliable analysis of… More >

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