Dynamical aspects of smoking model with cravings to smoke

Nonlinear engineering: Modeling and application

article

Aziz Ullah Awan¹  Attia Sharif¹  Kashif Ali Abro²  Muhammad Ozair³  Takasar Hussain³ 

[1] Department of Mathematics, University of the Punjab;Department of Mathematics, COMSATS University Islamabad, Attock Campus;Institute of Ground Water Studies, Faculty of Natural and Agricultural Sciences, University of the Free State;Department of Basic Sciences and Related Studies, Mehran University of Engineering and Technology;Permanent address:Department of Basic Sciences and Related Studies, Mehran University of Engineering and Technology

关键词: Square-root dynamics;    Cravings;    Global stability;    Graph-theoretic approach;    Optimal control;   

DOI  :  10.1515/nleng-2021-0008

来源: De Gruyter

【 摘 要 】

The square-root dynamics of smoking model with cravings to smoke, in which square root of potential smokers and smokers is the interaction term, has been studied. We categorized net population in four different chambers: non-smokers/potential smokers, smokers/infected people, non-permanent smokers/temporary quitters and the permanent quitters. By dynamical systems approach, we analyzed our model. Moreover, for proving the unique equilibrium point to be globally stable, we took help of graph theoretic approach. The sensitivity analysis of the model is performed through the diseased classes effectively to design reliable, robust and stable control strategies. The model is designed like optimal control trouble to find out importance of various control actions on our system that are insisted by the sensitivity analysis. We have applied two controls, which are the awareness campaign through the media transmission to control the potential smokers and temporary quit smokers to become smokers and the treatment of smokers. Analytical and numerical methods are utilized for ensuring presence of these two control actions.

【 授权许可】

Unknown