Desain Kontrol Optimal Imunisasi dan Karantina Terhadap Penyebaran Penyakit Campak dengan Adanya Treatment Menggunakan Metode Prinsip Minimum Pontryagin

Suryadinata, Wiky (2024) Desain Kontrol Optimal Imunisasi dan Karantina Terhadap Penyebaran Penyakit Campak dengan Adanya Treatment Menggunakan Metode Prinsip Minimum Pontryagin. Other thesis, Institut Teknologi Sepuluh Nopember.

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Abstract

Penyakit Campak merupakan suatu penyakit akut yang sangat menular disebabkan oleh virus campak golongan Paramyxovirus, dengan gejala awal berupa batuk, demam,mata merah/berair, ruam kulit, dan hidung berair. Pada penelitian ini, dilakukan modifikasi dan analisis model SIQR (Susceptible, Infected, Quarantined, Recovered) untuk mengetahui penyebaran penyakit campak. Hasil analisis kestabilan dari modifikasi model tersebut adalah model bersifat stabil di sekitar titik kesetimbangan bebas penyakit dan bersifat stabil di sekitar titik kesetimbangan endemik serta memiliki nilai bilangan reproduksi dasar 〖(R〗_0)<1. Hal ini menyebabkan terjadinya penyebaran penyakit campak sampai waktu tertentu hingga perlunya menambahkan kontrol vaksinasi dan treatment pada model SIQR untuk meminimumkan penyebaran. Kontrol tersebut dioptimalkan menggunakan Prinsip Minimum Pontryagin yang disimulasikan secara numerik menggunakan metode Runge Kutta Orde 4. Hasil penelitian menunjukkan bahwa pemberian kontrol pada model memperlambat laju perpindahan dari populasi individu rentan ke populasi individu terinfeksi, mengurangi populasi individu terinfeksi, dan peningkatan populasi individu sembuh lebih cepat dibandingkan dengan model tanpa kontrol. Oleh karena itu, penambahan kontrol pada model SIQR terbukti efektif dalam meminimalisir penyebaran penyakit campak.
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Measles is a highly contagious acute disease caused by the Paramyxovirus measles virus, with initial symptoms of cough, fever, red/watery eyes, skin rash, and runny nose. In this study, modification and analysis of the SIQR (Susceptible, Infected, Quarantined, Recovered) model were carried out to determine the spread of measles. The results of the stability analysis of the modified model are that the model is stable around the disease-free equilibrium point and is stable around the endemic equilibrium point and has a basic reproduction number value of(R_0 )<1 . This causes the measles disease to spread until a certain time, so it is necessary to add vaccination and treatment controls to the SIQR model to minimize the spread. The control is optimized using the Pontryagin Minimum Principle which is numerically simulated using the 4th Order Runge Kutta method. The results showed that providing control in the model slowed down the rate of movement from the population of susceptible individuals to the population of infected individuals, reduced the population of infected individuals, and increased the population of cured individuals faster than the model without control. Therefore, the addition of control to the SIQR model proved effective in minimizing the spread of measles.

Item Type:	Thesis (Other)
Uncontrolled Keywords:	Measles Disease, Model SIQR, Optimal Control, Pontryagin Minimum Principle, Model SIQR, Kontrol Optimal, Penyakit Campak, Prinsip Minimum Pontryagin
Subjects:	Q Science > QA Mathematics > QA141 Numeracy--Problems, exercises, etc. 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 > QA401 Mathematical models.
Divisions:	Faculty of Science and Data Analytics (SCIENTICS) > Mathematics > 44201-(S1) Undergraduate Thesis
Depositing User:	Wiky Suryadinata
Date Deposited:	06 Aug 2024 03:45
Last Modified:	06 Aug 2024 03:45
URI:	http://repository.its.ac.id/id/eprint/113180

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