Pengendalian Optimal Terhadap Penyebaran Pneyakit Campak Menggunakan Metode Minimum Pontryagin

Haryono, Widiya Intan Ayu (2019) Pengendalian Optimal Terhadap Penyebaran Pneyakit Campak Menggunakan Metode Minimum Pontryagin. Other thesis, Institut Teknologi Sepuluh Nopember.

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Abstract

Campak merupakan peyakit menular yang disebabkan oleh virus Paramyxovirus. Virus tersebut termasuk kedalam famili dari genus morbillivirus. Tugas Akhir ini membahas tentang analisis pada model dengan menentukan bilangan reproduksi dasar, titik kesetimbangan bebas penyakit dan endemik, dan kestabilan dari setiap titik kesetimbangan berdasarkan kriteria Routh-Hurwitz. Kemudian dilakukan kontrol optimal dengan menggunakan Prinsip Minimum Pontryagin dengan kontrol ε berupa vakasinasi pertama dan θ berupa vaksinasi kedua yang bertujuan untuk meminimumkan jumlah individu yang terinfeksi. Pada hasil simulasi numerik menunjukkan bahwa pemberian kendali optimal vaksinasi dapat menurunkan proporsi individu yang terinfeksi penyakit campak.
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Measles is an infectious disease caused by the Paramyxovirus virus. The virus belongs to the family of the genus morbillivirus. This Final Project discusses the analysis of the model by determining basic reproductive numbers, disease free equilibrium points, endemic equilibrium points, and stability from each equilibrium point based on Routh-Hurwitz criteria. Then optimal control was carried out by using the Pontryagin Minimum Principle with the control ε in the form of the first vaccination and θ in the form of a second vaccination aimed at minimizing the number of infected individuals. In the numerical simulation results show that giving optimal control of vaccination can reduce the proportion of individuals infected with measles.

Item Type:	Thesis (Other)
Uncontrolled Keywords:	Vaksinasi, Kontrol Optimal, Prinsip Minimum Pontryagin
Subjects:	Q Science Q Science > QA Mathematics Q Science > QA Mathematics > QA278.3 Structural equation modeling. Q Science > QA Mathematics > QA402 System analysis.
Divisions:	Faculty of Mathematics, Computation, and Data Science > Mathematics > 44201-(S1) Undergraduate Thesis
Depositing User:	Widiya Intan Ayu Haryono
Date Deposited:	10 Aug 2026 06:29
Last Modified:	10 Aug 2026 06:29
URI:	http://repository.its.ac.id/id/eprint/66298

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