Desain Kendali Optimal Pada Model Penyebaran Penyakit Difteri Menggunakan Metode Prinsip Minimum Pontryagin

Afnani, Lintang Hayu Nur (2021) Desain Kendali Optimal Pada Model Penyebaran Penyakit Difteri Menggunakan Metode Prinsip Minimum Pontryagin. Undergraduate thesis, Institut Teknologi Sepuluh Nopember.

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Abstract

Difteri merupakan penyakit menular berbahaya yang disebabkan oleh bakteri Corynebacterium diphtheriae. Meskipun demikian, difteri dapat dicegah dengan imunisasi atau vaksinasi. Oleh karena itu, pada tugas akhir ini dilakukan desain kendali pada model penyebaran penyakit difteri menggunakan model SVIR dengan variabel kendali berupa pencegahan (penyuluhan imunisasi) dan pengobatan terhadap individu yang terinfeksi yang bertujuan untuk mengoptimalkan proporsi individu yang divaksinasi serta mengurangi banyaknya individu yang terinfeksi. Permasalahan kendali optimal tersebut diselesaikan menggunakan metode Prinsip Minimum Pontryagin untuk menemukan solusi secara analitik dan metode Runge-Kutta orde 4 untuk menyelesaikan sistem persamaan secara numerik. Hasil simulasi numerik menunjukkan menurunnya jumlah individu yang terinfeksi penyakit difteri setelah diberikan kendali berupa penyuluhan imunisasi dan pengobatan dengan persentase reduksi sebesar 100% selama 60 hari. ===================================================================================================== Diphtheria is a dangerous infectious disease caused by the bacterium Corynebacterium diphtheriae. However, diphtheria can be prevented by immunization or vaccination. Therefore, in this final project, a control design was carried out on the diphtheria spread model using SVIR models with control variables in the form of prevention (immunization campaign) and treatment of infected individuals to optimize the proportion of individuals who were vaccinated and reduce the number of infected individuals. The optimal control problem is solved using the Pontryagin Minimum Principle method to find a solution analytically and the Runge-Kutta 4th order method to solve the system of equations numerically. The results of numerical simulations showed a decrease in the number of individuals infected with diphtheria after providing controls in the form of immunization campaign and treatment with a reduction percentage of 100% for 60 days.

Item Type: Thesis (Undergraduate)
Uncontrolled Keywords: Difteri, Model SVIR, Prinsip Minimum Pontryagin, Runge-Kutta, Diphtheria, SVIR Models, Pontryagin Minimum Principle
Subjects: Q Science > QA Mathematics > QA278.3 Structural equation modeling.
Q Science > QA Mathematics > QA371 Differential equations--Numerical solutions
Q Science > QA Mathematics > QA372.B9 Differential equations--Numerical solutions. Runge-Kutta formulas--Data processing.
Q Science > QA Mathematics > QA614.8 Differentiable dynamical systems
Divisions: Faculty of Science and Data Analytics (SCIENTICS) > Mathematics > 44201-(S1) Undergraduate Thesis
Depositing User: Lintang Hayu Nur Afnani
Date Deposited: 24 Aug 2021 00:18
Last Modified: 24 Aug 2021 00:18
URI: https://repository.its.ac.id/id/eprint/89967

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