Kontrol Optimal Model Penyebaran Kanker Paru Akibat Merokok Menggunakan Prinsip Minimum Pontryagin

Hidayati, Zakiya Alfi (2023) Kontrol Optimal Model Penyebaran Kanker Paru Akibat Merokok Menggunakan Prinsip Minimum Pontryagin. Other thesis, Institut Teknologi Sepuluh Nopember.

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Abstract

Kanker paru termasuk penyakit paling mematikan di dunia yang 80% dari seluruh kasusnya disebabkan oleh aktivitas merokok. Perokok aktif memiliki kemungkinan yang tinggi untuk terinfeksi kanker paru begitu juga bagi perokok pasif. Meskipun demikian, jumlah perokok aktif dan perokok pasif di Indonesia masih terus meningkat dan perlu penanganan yang maksimal. Oleh karena itu, pada penelitian ini akan dibahas mengenai pemberian kontrol yang optimal untuk menekan angka perokok aktif, perokok pasif, sekaligus penderita kanker paru, menggunakan model SEIR (Susceptible-Exposed-Infected-Removed). Model yang digunakan merupakan hasil modifikasi dari model yang sudah ada dengan menambahkan asumsi bahwa orang yang telah sembuh dari kanker paru tidak dapat kembali menjadi rentan. Upaya untuk menekan angka perokok aktif salah satunya dengan layanan konseling berhenti merokok dan
untuk menekan angka perokok pasif yaitu dengan membatasi interaksi antara perokok aktif dengan populasi Susceptible dengan menetapkan dan menertibkan Kawasan Tanpa Rokok (KTR). Kontrol optimal ditentukan dengan Prinsip Minimum Pontryagin dan diselesaikan secara numerik menggunakan metode Runge-Kutta orde empat pada Matlab. Dari analisis hasil simulasi, diperoleh bahwa populasi perokok aktif dan pasif akan menurun lebih cepat setelah diberikan kontrol. Hal ini juga mengakibatkan populasi penderita kanker paru juga menurun.
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Lung cancer is among the deadliest diseases in the world with 80% of all cases caused by smoking. Active smokers have a high probability of becoming infected with lung cancer
as well as passive smokers. Nevertheless, the number of active smokers and passive smokers in Indonesia is still increasing and needs maximum treatment. Therefore, this study discussed the provision of optimal controls to reduce the number of active smokers, passive smokers, as well as lung cancer patients, using the SEIR (Susceptible-Exposed-Infected-Removed) model. The model used is the result of the development of an existing model by adding the assumption that people who have recovered from lung cancer cannot return to being Susceptible. One of the efforts to reduce the number of active smokers is through smoking cessation counseling services and to reduce the number of passive smokers, by limiting the interaction between active smokers and the Susceptible population by establishing and controlling Smoking Free Areas (KTR). The optimal control was determined by the Pontryagin’s Minimum Principle and completed numerically using the fourth-order Runge-Kutta method on the Matlab. From the simulation results, it was found that the population of active and passive smokers would decrease faster after being given control. This has also resulted in a decrease in the population of lung cancer sufferers.

Item Type:	Thesis (Other)
Uncontrolled Keywords:	Kanker Paru, model SEIR, Prinsip Minimum Pontryagin. Lung Cancer, Pontryagin’s Minimum Principle, SEIR model
Subjects:	Q Science > Q Science (General) > Q180.55.M38 Mathematical models Q Science > QA Mathematics > QA372.B9 Differential equations--Numerical solutions. Runge-Kutta formulas--Data processing. Q Science > QA Mathematics > QA401 Mathematical models. R Medicine > RA Public aspects of medicine > RA653.5 Epidemics
Divisions:	Faculty of Science and Data Analytics (SCIENTICS) > Mathematics > 44201-(S1) Undergraduate Thesis
Depositing User:	Zakiya Alfi Hidayati
Date Deposited:	03 Aug 2023 04:22
Last Modified:	03 Aug 2023 04:22
URI:	http://repository.its.ac.id/id/eprint/100730

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