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Title: | Analisis Kestabilan Model SEIR COVID-19 dengan Pengaruh Vaksinasi |
Authors: | Jaharuddin Kusnanto, Ali Andareksa, Rimba |
Issue Date: | 2023 |
Publisher: | IPB University |
Abstract: | Corona Virus Disease atau COVID-19 adalah penyakit menular yang cukup
serius bagi kesehatan masyarakat. COVID-19 merupakan penyakit yang
disebabkan oleh virus SARS-CoV-2. Tujuan dari penelitian ini adalah menentukan
serta menganalisis kestabilan dari titik tetap pada model SEIR COVID-19 dan
melakukan simulasi numerik untuk mengkaji pengaruh vaksinasi. Analisis
kestabilan titik tetap ditentukan dengan aturan Descartes dan fungsi Lyapunov.
Bilangan reproduksi dasar (ℛ0) didapatkan dengan menggunakan matriks next
generation. Hasil penelitian ini menunjukkan bahwa titik tetap bebas penyakit
bersifat stabil asimtotik bilamana ℛ0 < 1. Simulasi numerik dilakukan dengan
menggunakan software Mathematica 13.0. untuk mengetahui pengaruh parameter
terhadap bilangan reproduksi dasar. Penurunan laju perpindahan populasi individu
terpapar ke populasi individu terinfeksi mengakibatkan bilangan reproduksi dasar
menurun. Kenaikan tingkat pemberian vaksinasi pada populasi individu rentan akan
mengakibatkan bilangan reproduksi dasar menurun. Dengan mengontrol kedua
parameter tersebut, penyebaran penyakit akan dapat dikendalikan. Corona Virus Disease or COVID-19 is an infectious disease that is quite serious for public health. COVID-19 is a disease caused by the SARS- CoV-2 virus. The purpose of this study is to determine and analyze the stability of equilibrium points in the COVID-19 SEIR model and conduct numerical simulations to assess the effect of vaccination. The analysis of equilibrium-point stability is determined by Descartes' rule and the Lyapunov function. The basic reproduction number (ℛ0) is obtained using the next generation matrix. The results of this study show that disease-free fixed points are asymptotic stable when ℛ0 < 1. Numerical simulations were carried out using Mathematica 13.0 software to find out the effect of parameters on the basic reproductive number. A decrease in population movement rate of the population of exposed individuals to the population of infected individuals causes a decrease in the basic reproductive number. An increase vaccination rate in vulnerable individual populations will causes a decrease in the basic reproductive number. By controlling parameters, the spread of the disease will be controlled. |
URI: | http://repository.ipb.ac.id/handle/123456789/120166 |
Appears in Collections: | UT - Mathematics |
Files in This Item:
File | Description | Size | Format | |
---|---|---|---|---|
Cover, Lembar Pernyataan, Abstrak, Lembar Pengesahan, Prakata dan Daftar Isi.pdf Restricted Access | Cover | 467.69 kB | Adobe PDF | View/Open |
G54180067_Rimba Andareksa.pdf Restricted Access | Fulltext | 884.75 kB | Adobe PDF | View/Open |
Lampiran.pdf Restricted Access | Lampiran | 2.24 MB | Adobe PDF | View/Open |
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