Musa, Muhammad (2015) Analisis kestabilan dan bifurkasi mundur pada model infeksi virus hepatitis B dan C pada tubuh pasien. Undergraduate thesis, Institut Teknologi Sepuluh Nopember.
Preview |
Text
1211100070-Undergraduate.pdf Download (1MB) | Preview |
Abstract
Penyakit hepatitis merupakan penyakit yang menyerang
hati manusia disebabkan oleh virus hepatitis, antara lain
virus Hepatitis B dan C . Tugas Akhir ini membahas
tentang analisis pada model infeksi virus hepatitis B dan C
pada tubuh pasien atau penderita dengan menyelidiki adanya
kestabilan dari setiap titik kesetimbangan, kestabilan global
pada titik kesetimbangan bebas penyakit, menentukan bilangan
reproduksi dasar, bifurkasi, dan solusi numerik dari model
dinamik menggunakan metode Runge-Kutta orde empat dan
simulasinya. Hasil analisis menunjukkan adanya kestabilan
pada setiap titik kesetimbangan, kestabilan global pada titik
kesetimbangan bebas penyakit, dan bifurkasi mundur dalam
model. Adanya bifurkasi mundur disebabkan ketidakefektifan
pengobatan transplantasi hati sehingga masih terdapat titik
kesetimbangan endemik pada saat bilangan reproduksi dasar
kurang dari 1. Sedangkan dari simulasi numerik dengan
Metode Runge Kutta orde empat diperoleh grafik kestabilan
yang akurat dengan error kecil dari setiap titik kesetimbangan
berdasarkan nilai bilangan reproduksi dasar.
=====================================================================================================
Hepatitis is a disease which attack human liver because
of hepatitis virus. Two types of Hepatitis virus are Hepatitis
B and C. This final project explain the analysis on model
infectious hepatitis B and C virus in patient body to investigate
the stability of each equilibrium point, global stability of
disease free equilibrium, determine the basic reproduction
number, bifurcation, and numerical solution of the dynamic
models with Runge-Kutta fourth order methods then it’s
simulated. The analysis results indicates the existence of
the stability of each equilibrium point, global stability of
disease free equilibrium, and backward bifurcation on the
model. The existence of backward bifurcation caused by liver
transplantation is not effective therefore endemic equilibrium
point still exist when the basic reproduction number below
one. Meanwhile the numerical simulation with the Runge
Kutta method of fourth order is obtained an accurate chart
of stability with a small error from each point of equilibrium
based on the value of the basic reproduction number.
| Item Type: | Thesis (Undergraduate) |
|---|---|
| Additional Information: | RSMa 515.352 Mus a |
| Uncontrolled Keywords: | Epidemic model; Backward bifurcation; Basic Reproduction Number; Runge Kutta fourth order method |
| Subjects: | H Social Sciences > HD Industries. Land use. Labor > HD30.23 Decision making. Business requirements analysis. |
| Divisions: | Faculty of Mathematics, Computation, and Data Science > Mathematics > 44201-(S1) Undergraduate Thesis |
| Depositing User: | - Taufiq Rahmanu |
| Date Deposited: | 18 Jun 2019 03:06 |
| Last Modified: | 18 Jun 2019 03:06 |
| URI: | http://repository.its.ac.id/id/eprint/63141 |
Actions (login required)
 |
View Item |