Parouq, Abdullah Ihsan (2025) Analisis Kestabilan Model SIR Tanpa Vaksinasi Menggunakan Fungsi Lyapunov. Other thesis, Institut Teknologi Sepuluh Nopember.
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Abstract
Kestabilan sistem dinamik merupakan topik penting dalam berbagai disiplin ilmu, terutama fisika dan matematika. Salah satu metode analisis kestabilan yang umum digunakan adalah Fungsi Lyapunov, yang memungkinkan evaluasi kestabilan tanpa memerlukan solusi eksplisit dari persamaan diferensial. Penelitian ini bertujuan untuk menganalisis kestabilan sistem Model SIR yang merupakan sistem non-linear, dengan menggunakan Fungsi Lyapunov. Metode ini diterapkan untuk memeriksa kestabilan dinamik pada masing-masing titik setimbang. Penelitian kali ini menggunakan model penyebaran yang tidak menggunakan vaksinasi pada parameter model. Hasilnya didapat dua titik kesetimbangan, berupa titik kesetimbangan bebas infeksi dan titik kesetimbangan endemik.
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The stability of dynamical systems is an important topic in various disciplines, especially physics and mathematics. One of the commonly used stability analysis methods is the Lyapunov Function, which allows stability evaluation without requiring explicit solutions of differential equations. This study aims to analyze the stability of the SIR Model system, which is a non-linear system, using the Lyapunov Function. This method is applied to examine the dynamic stability at each equilibrium point. The results obtained two equilibrium points, namely an infection-free equilibrium point and an endemic equilibrium point.
| Item Type: | Thesis (Other) |
|---|---|
| Uncontrolled Keywords: | Analisis Kestabilan, Bilangan Reproduksi, Fungsi Lyapunov, Titik Kesetimbangan, Stability Analysis, Reproduction Number, Lyapunov Function, Equilibrium Point. |
| Subjects: | Q Science > QA Mathematics > QA402 System analysis. |
| Divisions: | Faculty of Science and Data Analytics (SCIENTICS) > Mathematics > 44201-(S1) Undergraduate Thesis |
| Depositing User: | Abdullah Ihsan Parouq |
| Date Deposited: | 04 Aug 2025 07:45 |
| Last Modified: | 09 Oct 2025 07:24 |
| URI: | http://repository.its.ac.id/id/eprint/125621 |
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