Harmonic mean type dynamics of a delayed giving up smoking model and optimal control strategy via legislation. Issue 15 (October 2020)

• Record Type: Journal Article
• Authors: Zhang, Zizhen; ur Rahman, Ghaus; Agarwal, Ravi P.
• Is Part Of: Journal of the Franklin Institute. Volume 357:Issue 15(2020)
• Page Start: 10669
• Page End: 10690
• Publication Date: 2020-10
• Subjects: Science -- Periodicals; Technology -- Periodicals; Patents -- United States -- Periodicals; 505
• DOI: 10.1016/j.jfranklin.2020.09.002
• Languages: English
• ISSNs: 0016-0032

Abstract

Highlights: To formulate a model for studying the dynamics of giving up smoking model. To incorporate delay term due to the fact that a certain period is required for the occasional smokers need to develop into the chain smokers. To explore existence of local stability and Hopf bifurcation. To explore new controls in the form of legislation. To carry out numerical simulations for the obtained results. Abstract: In this research work, a delayed giving up smoking model is initially formulated. The model is obtained by dividing the whole population into measurable partitions of four subclasses as well as taking into account harmonic mean type of incidence rate. For the existence of local stability and Hopf bifurcation, some sufficient conditions are derived by incorporating time delay as a bifurcation parameter. Directly afterward, direction and stability of the Hopf bifurcation are investigated. Moreover, using the optimal control strategy in the form of legislation, we propose optimal strategies to lower down the number of smokers. An optimal control solution is obtained for the control problem. In order to characterize the optimal controls, Pontryagin's maximum principle with time delay is used as the main tool.