A passive verses active exposure of mathematical smoking model: A role for optimal and dynamical control

Author:

Hussain Takasar1,Awan Aziz Ullah2,Abro Kashif Ali34,Ozair Muhammad1,Manzoor Mehwish1,Gómez-Aguilar José Francisco5,Galal Ahmed M.67

Affiliation:

1. Department of Mathematics, COMSATS University Islamabad, Attock Campus , Attock , Pakistan

2. Department of Mathematics, University of the Punjab , Lahore 54590 , Pakistan

3. Institute of Ground Water Studies, Faculty of Natural and Agricultural Sciences, University of the Free State , Bloemfontein , South Africa

4. Department of Basic Sciences and Related Studies, Mehran University of Engineering and Technology , Jamshoro , Pakistan

5. CONACyT-Tecnológico Nacional de México/CENIDET, Interior Internado Palmira S/N, Col. Palmira, C.P. 62490 , Cuernavaca , Morelos , Mexico

6. Department of Mechanical Engineering, College of Engineering, Prince Sattam bin Abdulaziz University , Wadi addawaser 11991 , Saudi Arabia

7. Production Engineering and Mechanical Design Department, Faculty of Engineering, Mansoura University , P.O 35516 , Mansoura , Egypt

Abstract

Abstract Smoking has become one of the major causes of health problems around the globe. It harms almost every organ of the body. It causes lung cancer and damage of different muscles. It also produces vascular deterioration, pulmonary disease, and ulcer. There is no advantage to smoking except the monetary one to the tobacco producers, manufacturers, and advertisers. Due to these facts, a passive verse active exposure of mathematical smoking model has been analyzed subject to the dynamical aspects for giving up smoking. In this context, mathematical modelling and qualitative analysis have been traced out for smoking model having five classes. Mathematical forms of smoke absent and smoke present points of equilibrium have been calculated for knowing optimal and dynamical control. By making use of the Lyapunov function theory, we have shown the global asymptotic behavior of smoke-free equilibrium for threshold parameter R 0 < 1 {R}_{0}\lt 1 . The ability to observe theoretically and through graphs is invoked to study the general behavior of single smoke present point. To make effective, vigorous, authentic, and stable strategies to control the disease, we have performed the sensitivity examination of threshold parameter and disease, present apartments.

Publisher

Walter de Gruyter GmbH

Subject

Computer Networks and Communications,General Engineering,Modeling and Simulation,General Chemical Engineering

Reference63 articles.

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