Optimal control of smoking cessation programs for two subclasses of smoker

Volume 31, Issue 1, pp 41--55 http://dx.doi.org/10.22436/jmcs.031.01.04

Publication Date: April 04, 2023 Submission Date: August 10, 2022 Revision Date: December 16, 2022 Accteptance Date: February 16, 2023

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Authors

R. Herdiana - Department of Mathematics, Faculty of Science and Mathematics, Universitas Diponegoro, Semarang 50275, Indonesia. H. Tjahjana - Department of Mathematics, Faculty of Science and Mathematics, Universitas Diponegoro, Semarang 50275, Indonesia. A. Henindya - Department of Mathematics, Faculty of Science and Mathematics, Universitas Diponegoro, Semarang 50275, Indonesia. N. S. A. Latif - Faculty of Computer Science and Mathematics, Universiti Teknologi MARA, 40450 Shah Alam, Selangor, Malaysia.

Abstract

In this paper, we propose a dynamic system model representing the interaction between smokers in mixed populations of beginners and regular/heavy smokers and incorporate a smoking cessation program. Since not all smokers acquire treatments, we divide each subclass, beginners and smokers, into untreated and treated groups. From the mathematical analysis, we obtained the basic reproduction number, which is the condition for the smoking-free and endemic equilibriums. This study focuses on two intervention programs as control variables to reduce the smoking habit of smokers, namely educational campaigns for the subclass of beginners and counselling with nicotine therapy for the second subclass of regular/heavy smokers. The objective of the control strategy is to minimize the number of individuals in both subclasses of smokers and maximize the number of quitters with minimum cost. The existence of a solution to the optimal control problem is derived using Pontryagin's maximum principle. The numerical simulations are conducted to visualise and confirm the analytical results, which show the effectiveness of the treatments in reducing the number of smokers. Compared to mono-therapy, the combination therapy of educational campaigns and counselling with nicotine replacement is more effective in reducing the number of smokers.

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Keywords

• Smoking cessation
• equilibrium
• optimal control
• Pontryagin's maximum principle

MSC

•  34K35
•  49J15
•  49K15

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