Threshold dynamics and optimal control of an age-structured giving up smoking model. (October 2018)

• Record Type: Journal Article
• Authors: ur Rahman, Ghaus; Agarwal, Ravi P.; Liu, Lili; Khan, Asaf
• Is Part Of: Nonlinear analysis. Volume 43(2018)
• Page Start: 96
• Page End: 120
• Publication Date: 2018-10
• Subjects: Giving up smoking model -- Age factor -- Smoking generation number -- Global stability -- Optimal control -- Gateaux derivative; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2018.02.006
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: In this paper, a new giving up smoking model is proposed by incorporating the continuous age-structure in the chain smokers class, which is known as a class of age-structured giving up smoking model. Smoking generation number is defined and proved to be a classic threshold parameter. Two steady states of the model are found. The corresponding characteristic equations are analyzed, and the proper Lyapunov functionals are constructed to show the local and global stability of both steady states. Optimal control strategy is presented and numerical simulations are made to support the main results. Highlights: A new giving up smoking model with the continuous age-structure in the chain smokers class is proposed. Local and global stabilities are studied to establish strict threshold dynamics. The optimal control strategy on potential smokers is proposed. Numerical simulations on dynamical results and optimal control are performed.