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Aug 31, 2023
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Apr 5, 2024
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Abstract

Pemodelan matematika dalam bentuk persamaan diferensial mampu menggambarkan fenomena atau kejadian yang terjadi disekitar kita. Fenomena yang dibahas pada penelitian ini berupa model matematika interaksi antara perokok konvensional dan elektrik. Dimana, langkah yang dilakukan dengan melakukan rekrontuksi model matematika populasi perokok konvensional dan perokok elektrik dengan menerapkan teori dan konsep kontrol optimal. Adapun variabel-variabel kontrol yang ditambahkan pada model berjumlah empat, yaitu  dan  Variabel kontrol  dan  merepresentasikan tentang pemberian edukasi kepada masyarakat awam yang berpotensi untuk merokok, dan bahaya akibat menjadi perokok pasif ketika berinteraksi dengan perokok konvensional atau perokok elektrik. Sedangkan kontrol  dan  merepresentasikan tentang edukasi akan pentingnya manfaat untuk berhenti dari kebiasaan merokok konvensional maupun merokok elektrik. Harapan serta ujuan dari masalah kontrol optimal ini adalah untuk meminimkan jumlah populasi yang merokok secara konvensional maupun merokok elektrik. Melalui implementasi prinsip minimum Pontryagin pada model yang akan diselesaikan, maka didapatkan kondisi-kondisi tertentu untuk masalah kontrol optimal. Selanjutnya, sebagai pendukung dari analisis yang telah diperoleh, maka diberikan simulasi numerik dengan bantuan software Matlab. Bagian akhir simulasi diperlihatkan bahwa variabel kontrol dan bobot kontrol yang diterapkan pada model mampu mengurangi atau meminimumkan jumlah populasi yang merokok secara konvensional maupun elektrik.


Mathematical modeling in the form of differential equations is able to describe phenomena that occur around us. The phenomenon discussed in this study is a mathematical model of the interaction between conventional and electric smokers. Where, the steps taken are to perform a mathematical model reconstruction of the population of conventional smokers and electric smokers by applying the optimal control problem. There are four control variables added to the model, namely , , , and . The variables  and  represent of education to ordinary people who have the potential to smoke, and the dangers of being a passive smoker when interacting with conventional smokers or electric smokers. While the  and  controls represent education about the importance of the benefits of quitting conventional smoking and electric smoking. The hope and goal of this optimal control problem is to minimize the number of populations who smoke conventionally or electric cigarettes. Through the implementation of Pontryagin's minimum principle in the model to be solved, certain conditions for optimal control problems are obtained. Furthermore, as a support for the analysis that has been obtained, a numerical simulation is given with the help of MATLAB software. The final part of the simulation shows that the control variables and control weights applied to the model are able to reduce or minimize the number of populations who smoke conventionally or electrically.

Keywords

perokok konvensional, perokok elektrik, kontrol optimal, kaidah pontryagin, simulasi mumerik

Article Details

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