Paulina, Ezra Christine (2017) Analisis Perluasan Model Epidemi Hiv/Aids Dengan Pengobatan. Sarjana thesis, Universitas Brawijaya.
Abstract
Pada Skripsi ini dibahas perluasan model epidemi HIV/AIDS dengan pengobatan. Model diperluas dengan menambahkan tingkat kejadian infeksi umum yang dinotasikan dengan . Perilaku model epidemi sangat dipengaruhi oleh tingkat kejadian infeksi, yaitu laju individu rentan menjadi individu terinfeksi akibat kontak langsung dengan individu terinfeksi. Analisis yang dilakukan pada model meliputi penentuan titik kesetimbangan, angka reproduksi dan analisis kestabilan titik kesetimbangan. Fungsi Lyapunov digunakan untuk menganalisis kestabilan global titik kesetimbangan. Hasil analisis diketahui bahwa model mempunyai dua titik kesetimbangan, yaitu titik kesetimbangan bebas penyakit dan titik kesetimbangan endemi. Jika , maka hanya terdapat satu titik kesetimbangan, yaitu titik kesetimbangan bebas penyakit. Jika , maka terdapat dua titik kesetimbangan yaitu titik kesetimbangan bebas penyakit dan titik kesetimbangan endemi. Analisis kestabilan menunjukan bahwa titik kesetimbangan bebas penyakit akan stabil asimtotik lokal jika dan stabil global jika , sedangkan titik kesetimbangan endemi akan stabil asimtotik global jika .
English Abstract
An extended epidemic models HIV/AIDS with treatment is discussed in this final project. The model is extended by addition of general incidence rate, denoted by The behavior of epidemic model is affected by incidence rate, that is, the number of new cases of infection per unit time. Analysis of the model covers the determination of equilibrium points, basic reproduction number, stability analysis of equilibrium points. Lyapunov fuctions is used to analyzed the global stability of equilibrium points. The analysis shows that the model has two equilibrium points, which are the disease free equilibrium point and the endemic equilibrium point. If then there is only one equilibrium point that exists, which is the disease-free equilibrium point. If then there are two equilibrium points that exist, which is the disease-free equilibrium point and the endemic equilibrium point. Stability analysis shows that the disease free equilibrium point is locally asymptotically stable if and it is globally stable if , while the endemic equilibrium point is globally asymptotically stable if .
| Item Type: | Thesis (Sarjana) |
|---|---|
| Identification Number: | SKR/FMIPA/2017/419/051709759 |
| Uncontrolled Keywords: | HIV/AIDS, tingkat kejadian, angka reproduksi dasar, fungsi Lyapunov |
| Subjects: | 500 Natural sciences and mathematics > 515 Analysis > 515.3 Differential calculus and equations > 515.35 Differential equations |
| Divisions: | Fakultas Matematika dan Ilmu Pengetahuan Alam > Matematika |
| Depositing User: | Nur Cholis |
| Date Deposited: | 17 Oct 2017 07:07 |
| Last Modified: | 22 Nov 2021 03:42 |
| URI: | http://repository.ub.ac.id/id/eprint/3838 |
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