Lamis, Atikah (2019) Analisis Dinamik Model Penyebaran Rumor dengan Kontrol Optimal pada Penayangan Berita di Media. Sarjana thesis, Universitas Brawijaya.
Abstract
Pada skripsi ini dibahas model penyebaran rumor dengan kontrol optimal pada penayangan berita di media, model tersebut dianalogikan sebagai model penyebaran penyakit. Pada model dilakukan analisis dinamik yang meliputi penentuan titik kesetimbangan, angka reproduksi dasar (R0), dan analisis kestabilan lokal. Hasil analisis dinamik menunjukkan bahwa model memiliki dua titik kesetimbangan, yaitu titik kesetimbangan bebas rumor dan titik kesetimbangan endemik. Kestabilan titik kesetimbangan bebas rumor dan eksistensi titik kesetembangan endemik bergantung pada R0. Jika R0 < 1, maka titik kesetimbangan bebas rumor stabil asimtotik lokal dan jika R0 > 1, maka titik kesetimbangan endemik eksis. Titik kesetimbangan endemik stabil asimtotik lokal jika memenuhi kriteria Routh-Hurwitz. Simulasi numerik dilakukan untuk memverifikasi hasil analisis dinamik yang telah dilakukan. Selanjutnya, dilakukan kontrol optimal pada penayangan berita di media untuk meminimumkan fungsi tujuan, masalah kontrol optimal tersebut diselesaikan dengan menggunakan prinsip Minimum Pontryagin. Penyelesaian numerik dilakukan menggunakan metode Sweep Maju-Mundur untuk menunjukkan pengaruh dari pemberian kontrol
English Abstract
This thesis aims to discuss a dynamic analysis of a rumor spreading model with optimal control on news broadcasting in media, the model is analogized to the spread disease model. Dynamic analysis was performed to the model including determining equilibrium points, basic reproduction numbers (R0), and local stability analysis. The result of dynamic anaysis shows that the model has two equilibrium points, namely rumor-free equilibrium point and endemic equilibrium point. The stability of the rumor-free equilibrium point and the existence of endemic equilibrium points depend on R0. If R0 < 1, then the rumor-free equilibrium point is stable locally asymptotically and if R0 > 1, the endemic equilibrium point is exist. The endemic equilibrium point is stable asymptotically if it fulfills the Routh-Hurwitz criteria. Numerical simulations were carried out to verify the results of the dynamic analysis that has been done. Furthermore, optimal control was performed on news broadcasts in the media to reduce the objective function, the optimal control problem was done by utilizing the Pontryagin Minimum principle. Numerical solutions were conducted by using the Sweep Forward-Backward method to show the effect of giving control.
Other obstract
-
| Item Type: | Thesis (Sarjana) |
|---|---|
| Identification Number: | SKR/MIPA/2019/253/051911033 |
| Uncontrolled Keywords: | penyebaran rumor, titik kesetimbangan, angka reproduksi dasar, analisis kestabilan lokal, kontrol optimal. spread of rumors, equilibrium points, basic reproduction numbers, local stability analysis, optimal control. |
| Subjects: | 500 Natural sciences and mathematics > 519 Probabilities and applied mathematics > 519.6 Mathematical optimization |
| Divisions: | Fakultas Matematika dan Ilmu Pengetahuan Alam > Matematika |
| Depositing User: | Budi Wahyono Wahyono |
| Date Deposited: | 10 Aug 2020 08:08 |
| Last Modified: | 21 Sep 2023 01:19 |
| URI: | http://repository.ub.ac.id/id/eprint/179567 |
![[thumbnail of Atikah Lamis.pdf]](http://repository.ub.ac.id/style/images/fileicons/text.png) |
Text
Atikah Lamis.pdf Download (2MB) |
Actions (login required)
 |
View Item |