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http://repository.ipb.ac.id/handle/123456789/109122
Title: | Analisis Kestabilan Model Epidemi pada Penyebaran Virus Hepatitis B dengan Vaksinasi |
Authors: | Jaharuddin Kusnanto, Ali Merdiani, Murni Ayu |
Issue Date: | Sep-2021 |
Publisher: | IPB University |
Abstract: | Virus hepatitis B adalah penyebab penyakit hepatitis B. Model epidemi
penyebaran virus hepatitis B dengan vaksinasi yang ditinjau adalah model SIR
(Susceptible, Infected, Recovered). Penelitian ini bertujuan untuk merekonstruksi
model, menentukan titik tetap dan bilangan reproduksi dasar, menganalisis
kestabilan titik tetap dan sensitivitas, serta melakukan simulasi numerik. Bilangan
reproduksi dasar diperoleh dengan menggunakan the next generation matrix.
Simulasi numerik dilakukan dengan menggunakan software Mathematica 12.0
untuk menunjukkan pengaruh setiap parameter terhadap bilangan reproduksi dasar.
Penurunan tingkat penularan mengakibatkan penurunan bilangan reproduksi dasar.
Kenaikan tingkat pemulihan dan vaksinasi mengakibatkan penurunan bilangan
reproduksi dasar. Perubahan bilangan reproduksi dasar berpengaruh pada
kestabilan sistem. Hepatitis B virus is the cause of hepatitis B disease. The epidemic model of the spread hepatitis B virus with vaccination is the SIR (Susceptible, Infected, Recovered) model. The purpose of this research is to reconstruct the model, determining the fixed point and the basic reproduction number, analysing the stability of the fixed point and sensitivity, and perform numerical simulations. The basic reproduction number is obtained using the next generation matrix. Numerical simulations are carried out using Mathematica 12.0 software to show the effect of each parameter on the basic reproduction number. The decrease in the transmission level implies the decrease in the basic reproduction number. The increase in the rate of recovery and vaccination implies the decrease in the basic reproduction number. The changes in the basic reproduction affect the stability of the system. |
URI: | http://repository.ipb.ac.id/handle/123456789/109122 |
Appears in Collections: | UT - Mathematics |
Files in This Item:
File | Description | Size | Format | |
---|---|---|---|---|
Cover.pdf | Cover | 379.09 kB | Adobe PDF | View/Open |
Draf Final TA a.n. Murni Ayu Merdiani_G54170017_WM.pdf Restricted Access | Fullteks | 14.93 MB | Adobe PDF | View/Open |
Lampiran.pdf Restricted Access | Lampiran | 3.01 MB | Adobe PDF | View/Open |
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