Permatasari, Dita Ayu (2019) Analisis Dinamik dan Kontrol Optimal Model Matematika Penyakit Layu Pinus. Sarjana thesis, Universitas Brawijaya.
Abstract
Pada skripsi ini dibahas analisis dinamik dan penerapan kontrol optimal pada model matematika penyakit layu pinus. Analisis dinamik yang dilakukan meliputi penentuan titik kesetimbangan, angka reproduksi dasar (ℛ0), dan analisis kestabilan global. Hasil analisis dinamik menunjukkan bahwa model memiliki dua titik kesetimbangan, yaitu titik kesetimbangan bebas penyakit dan titik kesetimbangan endemik. Titik kesetimbangan bebas penyakit selalu eksis, sedangkan titik kesetimbangan endemik eksis dengan syarat ℛ0>1. Kestabilan titik kesetimbangan bergantung pada nilai ℛ0. Jika ℛ0≤1, maka titik kesetimbangan bebas penyakit stabil asimtotik global dan jika ℛ0>1, maka titik kesetimbangan endemik stabil asimtotik global. Selanjutnya, dilakukan penerapan kontrol optimal untuk memaksimalkan subpopulasi pohon pinus rentan, dan meminimalkan subpopulasi pohon pinus exposed, pohon pinus terinfeksi, vektor rentan, vektor exposed, dan vektor terinfeksi. Kontrol yang digunakan, yaitu injeksi insektisida dan vaksinasi ke tubuh pohon pinus, deforestasi, dan penyemprotan insektisida di udara. Hasil simulasi numerik menunjukkan pemberian ketiga kontrol secara bersamaan memberikan hasil yang paling efektif dibandingkan dengan pemberian kombinasi dua kontrol saja.
English Abstract
This thesis discusses dynamical analysis and the application of optimal control to the mathematical model of pine wilt disease. Dynamical analysis carried out includes determining equilibrium points, basic reproduction numbers (ℛ0), and global stability analysis. The model has two equilibrium points, namely disease-free equilibrium point and endemic equilibrium point. Disease-free equilibrium point always exist, whereas endemic equilibrium point exist with conditions ℛ0>1. The stability of the equilibrium point depends on the value of ℛ0. If ℛ0≤1, then the disease-free equilibrium point is globally asymptotically stable and if ℛ0>1, then the endemic equilibrium point is globally asymptotically stable. Furthermore, optimal control is applied to maximize the subpopulation of susceptible pine trees, and minimize the subpopulation of exposed pine trees, infected pine trees, susceptible vectors, exposed vectors, and infected vectors. Control are used, namely injection of insecticides and vaccinations into the body of pine trees, deforestation, and spraying insecticides in the air. The numerical simulation results show that giving the three controls simultaneously provides the most effective results compared to giving a combination of just two controls.
Other obstract
-
| Item Type: | Thesis (Sarjana) |
|---|---|
| Identification Number: | SKR/MIPA/2019/82/051910785 |
| Uncontrolled Keywords: | penyakit layu pinus, titik kesetimbangan, angka reproduksi dasar, analisis kestabilan global, kontrol optimal. pine wilt disease, equilibrium point, basic reproduction number, global stability analysis, optimal control. |
| Subjects: | 500 Natural sciences and mathematics > 518 Numerical analysis > 518.2 Specific numerical methods |
| Divisions: | Fakultas Matematika dan Ilmu Pengetahuan Alam > Matematika |
| Depositing User: | Budi Wahyono Wahyono |
| Date Deposited: | 26 Aug 2020 04:42 |
| Last Modified: | 28 Oct 2021 02:03 |
| URI: | http://repository.ub.ac.id/id/eprint/176858 |
Preview |
Text
Dita Ayu Permatasari (3).pdf Download (2MB) | Preview |
Actions (login required)
 |
View Item |