Optimal Control on Smoking Behavior Spreading Model
with Education, Treatment, and Psychological Support

Ana Qubatun; Agus Widodo; Ummu Habibah

doi:https://doi.org/10.14445/22315373/IJMTT-V68I6P522

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 68 | Issue 6 | Year 2022 | Article Id. IJMTT-V68I6P522 | DOI : https://doi.org/10.14445/22315373/IJMTT-V68I6P522

Optimal Control on Smoking Behavior Spreading Model with Education, Treatment, and Psychological Support

Ana Qubatun, Agus Widodo, Ummu Habibah

Received	Revised	Accepted	Published
19 May 2022	30 Jun 2022	03 Jul 2022	08 Jul 2022

Abstract

The spreading phenomena of smoking behavior in the human population can be mathematically modeled. This research discusses the smoking behavior spreading model that consist of six subpopulations. The subpopulation of potential smokers is divided into two types, the first type is potential smokers who have not been educated, the second type is potential smokers who have been educated. The subpopulation of smokers consists of a light smokers subpopulation and a heavy smokers subpopulation. The subpopulation of smokers who quit smoking is divided into two types, the first type quit temporarily and the second type quit permanently. The model describes the rate of change of each subpopulation by being given three control variables, they are education, treatment, and psychological support which aimed to minimize light smokers subpopulation, heavy smokers subpopulation, and control implementation cost. Optimal control completion is using Pontryagin’s minimum principle. Then, the simulation is carried out by using the method of forward-backward sweep. The simulation results of numerical indicate that the application of combination oversee strategies education, treatment, and psychological support is effective to control the spread of smoking behavior and its implementation cost.

Keywords

Forward-backward sweep method, Numerical simulation, Optimal control, Pontryagin’s minimum principle, Smoking behavior model.

References

[1] A. Lahrouz, L. Omari, D. Kiouach, and A Belmaati, “Deterministic and Stochastic Stability of a Mathematical Model of Smoking,” Statistics & Probability Letters, vol. 81, no. 8, pp. 1276-1284, 2011.
[2] A. Sharma, and A.K. Misra, “Backward Bifurcation in a Smoking Cessation Model with Media Campaigns,” Applied Mathematical Modelling, vol. 39, pp. 1087-1098, 2015.
[3] F. Guerrero, F. J. Santonja, R. J. Villanueva, “Solving a Model for the Evolution OS Smoking Habit in Spain with Homotopy Analysis Method,” Nonlinear Analysis: Real World Applications, vol. 14, pp. 549-558, 2013.
[4] H.F. Huo, and C.C. Zhu, “Influence of Relapse in a Giving Up Smoking Model,” Abstract and Applied Analysis, vol. 525461, 2012.
[5] Labzai, A., O. Balatif, and M. Rachik, “Optimal Control Strategy for a Discrete Time Smoking Model with Spesific Saturated Incidence Rate,” Discrete Nature and Society, vol. 5949303, 2018.
[6] L. Pang, Z. Zhao, S. Liu, and X. Zhang, “A Mathematical Model Approach for Tobacco Control in China,” Applied Mathematics and Computation, vol. 259, pp. 497-509, 2015.
[7] G.C. Castillo, S.G. Jordan, and A.H. Rodriguez, “Mathematical Models for the Dynamics of Tobacco Use, Recovery, and Relapse,” Public Health, vol. 84, no. 4, pp. 543-547, 1997.
[8] C. Sun, and J. Jian, “Optimal Control of a Delayed Smoking Model with Immigration,” Journal of Biological Dynamics, vol. 13, no. 1, pp. 447-460, 2019.
[9] Kementrian Kesehatan RI, Perilaku Merokok Masyarakat Indonesia Berdasarkan Riskes-das 2007 dan 2013, INFODATIN Pusat Data dan Informasi Kementrian Kesehatan RI.
[10] O. Sharomi, and A.B. Gumel, “Indonesian Ministry of Health, Smoking Behavior of Indonesian Society Based on Riskes-das 2007 and 2013, INFODATIN Data and Information Center of the Indonesian Ministry of Health,” Curtailing Smoking Dynamics: A Mathematical Modeling Approach, Applied Mathematics and Computation, vol. 195, pp. 475-999, 2008.
[11] S. Durkin, E. Brennan, and M. Wakefeld, “Mass Media Campaigns to Promote Smoking Cessation among Adults: An Integrative Review,” Tob. Control, vol. 21, pp. 127-138, 2012.
[12] S. Lenhart, and J. T. Workman, “Optimal Control Applied to Biological Models”, Taylor & Francis Group, London, 2007.
[13] S. Tirtosastro, and A.S. Murdiyati, “Chemical Content of Tobacco and Cigarettes, Bulletin of Tobacco Plants”, Industrial Fibers and Oils,
[14] T. Aditama, Smoking and Health, Jakarta, UI Pers, vol. 2, no. 1, pp. 33-43, 2010.
[15] Z. Alkudhari, S. Al-Sheikh, and S. Al-Tuwairqi, “Global Dynamics of Mathematical Model on Smoking,” Applied Mathematics, vol. 847075, 2014.
[16] Z. Alkhudhari, S. Al-Sheikh, and S. Al-Tuwairqi, “Stability Analysis of a Giving Up Smoking Model,” International Journal of Applied Mathematical Research, vol. 3, pp. 168-177, 2014.
[17] Z. Alkhudhari, S. Al-Sheikh, and S. Al-Tuwairqi, “The Effect of Occasional Smokers on the Dynamics of a Smoking Model,” International Mathematical Forum, vol. 9, pp. 1207-1222, 2014.
[18] Z. Alkhudhari, S. Al-Sheikh, and S. Al-Tuwairqi, “The Effect of Heavy Smokers on the Dynamics of a Smoking Model,” International Journal of Differential Equation and Applications, vol. 14, pp. 343-356, 2015.

Citation :

Ana Qubatun, Agus Widodo, Ummu Habibah, "Optimal Control on Smoking Behavior Spreading Model with Education, Treatment, and Psychological Support," International Journal of Mathematics Trends and Technology (IJMTT), vol. 68, no. 6, pp. 173-179, 2022. Crossref, https://doi.org/10.14445/22315373/IJMTT-V68I6P522