Mawardi, Baiq Wentan Nida Anhofia (2024) Analisis Kestabilan dan Kontrol Optimal Model Penyebaran Populasi Perokok dengan Kontrol Penyuluhan (Edukasi) dan Permen Karet Nikotin. Other thesis, Institut Teknologi Sepuluh Nopember.
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Abstract
Rokok mengandung banyak senyawa kimia berbahaya yang dapat memberikan dampak buruk bagi tubuh baik bagi perokok maupun orang sekitar yang terpapar asap rokok. Dampak yang diberikan rokok menimbulkan kekhawatiran yang akhirnya memunculkan keinginan banyak perokok untuk berhenti merokok, namun tidak terealisasikan 100 %. Telah dilakukan penelitian mengenai model dan analisa penyebaran populasi perokok dengan menggunakan beberapa kontrol. Oleh karena itu, pada penelitian ini dikaji mengenai pengembangan model matematika penyebaran populasi perokok, titik kesetimbangan bebas perokok dan endemik, analisis kestabilan model dan analisis kontrol optimal. Masalah kontrol optimal diselesaikan menggunakan Prinsip Minimum Pontyagin untuk mendapatkan kontrol terbaik sistem dari keadaan awal sampai keadaan akhir. Kontrol yang digunakan pada penelitian ini ada dua, yaitu penyuluhan (edukasi) dan permen karet nikotin. Solusi numerik diselesaikan dengan metode Runge Kutta orde empat menggunakan software MATLAB. Berdasarkan hasil simulasi didapatkan bahwa pemberian kontrol berupa penyuluhan (edukasi) dan permen karet nikotin sebagai pengganti rokok dapat meminimumkan jumlah perokok ringan dan perokok berat serta memaksimumkan jumlah populasi yang berhenti merokok permanen
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Cigarettes contain many harmful chemical compounds that can have a negative impact on the body both for smokers and people around who are exposed to cigarette smoke. The impact given by cigarettes raises concerns that eventually lead to the desire of many smokers to quit smoking, but not realized 100 %. Research has been conducted on modeling and analyzing the distribution of the smoker population using several controls. Therefore, this study examines the development of a mathematical model of the spread of the population of smokers, the equilibrium point of smoker-free and endemic, the stability analysis of the model and the optimal control analysis. The optimal control problem is solved using the Pontyagin Minimum Principle to obtain the best control of the system from the initial state to the final state. There are two controls used in this study, namely counseling and nicotine gum. The numerical solution is solved by the fourth-order Runge Kutta method using MATLAB. Based on the simulation results, it is found that providing control in the form of counseling and nicotine gum as a substitute for cigarettes can minimize the number of light smokers and persistent smokers and maximize the number of people who quit smoking permanently.
| Item Type: | Thesis (Other) |
|---|---|
| Uncontrolled Keywords: | Analisis Kestabilan, Kontrol Optimal, Prinsip Minimum Pontryagin,Runge Kutta; System Stability, Optimal Control, Pontryagin Minimum Principle, Runge Kutta. |
| Subjects: | Q Science Q Science > QA Mathematics |
| Divisions: | Faculty of Science and Data Analytics (SCIENTICS) > Mathematics > 44201-(S1) Undergraduate Thesis |
| Depositing User: | Baiq Wentan Nida Anhofia Mawardi |
| Date Deposited: | 19 Feb 2024 04:38 |
| Last Modified: | 19 Feb 2024 04:38 |
| URI: | http://repository.its.ac.id/id/eprint/107504 |
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