Gifachri, Irawan (2018) Analisis Dinamik Model Influenza Dua Strain Virus dengan Dua Vaksinasi. Sarjana thesis, Universitas Brawijaya.
Abstract
Pada skripsi ini dibahas konstruksi dan analisis model influenza dua strain virus dengan dua vaksinasi. Pada model ini diasumsikan bahwa setiap individu hanya terinfeksi salah satu strain dan hanya memperoleh salah satu vaksin. Analisis yang dilakukan pada model meliputi penentuan titik kesetimbangan dan syarat eksistensinya, penentuan angka reproduksi dasar, dan analisis kestabilan global titik kesetimbangan menggunakan fungsi Lyapunov. Hasil analisis dinamik menunjukkan bahwa terdapat empat titik kesetimbangan pada model, yaitu titik kesetimbangan bebas penyakit, bebas penyakit strain 2, bebas penyakit strain 1, dan endemik. Titik kesetimbangan bebas penyakit selalu eksis sedangkan titik kesetimbangan bebas penyakit strain 2 dan bebas penyakit strain 1 eksis dengan syarat tertentu. Titik kesetimbangan endemik belum diketahui syarat eksistensinya sebab melibatkan dua persamaan yang saling bergantung. Terdapat dua angka reproduksi dasar pada model. Kestabilan tiga titik kesetimbangan bergantung pada kedua angka reproduksi dasar tersebut, sedangkan titik kesetimbangan endemik belum diketahui kestabilannya. Simulasi numerik yang dilakukan mendukung hasil analisis dinamik yang diperoleh.
English Abstract
This final project discusses the construction and analysis of a two-strain influenza model with two vaccinations. It is assumed that each individual is only infected by one of the strains and is obtained one of the vaccines. Dynamical analysis is performed by finding the equilibrium point and the existence condition of the equilibrium point, finding the basic reproduction number, and analyzing global stability of the equilibrium point. Dynamical analysis shows that there are four equilibrium points, namely disease-free point, strain 2 disease free point, strain 1 disease free point, and endemic point. Disease-free equilibrium point always exists while strain 2 disease free point and strain 1 disease free point exist under some conditions. The existence of the endemic point is still unknown because it involves two interdependent equations. Two basic reproduction numbers are found. The stability of three equilibrium points depends on those basic reproduction numbers, while the stability of the endemic point is still unknown. The result of numerical simulation supports the result of the dynamical analysis
| Item Type: | Thesis (Sarjana) |
|---|---|
| Identification Number: | SKR/MIPA/2018/478/051900407 |
| Uncontrolled Keywords: | influenza, dua strain, dua vaksin, angka reproduksi dasar, analisis kestabilan. influenza, two-strain, two vaccines, basic reproduction number, stability analysis. |
| Subjects: | 600 Technology (Applied sciences) > 615 Pharmacology and therapeutics > 615.3 Organics drugs > 615.37 Immunologic drugs and immune serums > 615.372 Vaccines |
| Divisions: | Fakultas Matematika dan Ilmu Pengetahuan Alam > Matematika |
| Depositing User: | Budi Wahyono Wahyono |
| Date Deposited: | 05 Jun 2020 06:50 |
| Last Modified: | 18 Oct 2021 06:44 |
| URI: | http://repository.ub.ac.id/id/eprint/168781 |
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