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

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

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.

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