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

  IJMTT-book-cover
 
International Journal of Mathematics Trends and Technology (IJMTT)
 
© 2022 by IJMTT Journal
Volume-68 Issue-6
Year of Publication : 2022
Authors : Ana Qubatun, Agus Widodo, Ummu Habibah
 10.14445/22315373/IJMTT-V68I6P522

How to Cite?

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, 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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