Hendarti, Nungky (2018) Analisis Dinamik Model Epidemi SEIS dengan Dampak Media. Sarjana thesis, Universitas Brawijaya.
Abstract
Pada skripsi ini, dibahas analisis dinamik model epidemi SEIS dengan dampak media. Pada model ini, populasi dibagi menjadi tiga subpopulasi, yaitu subpopulasi rentan (S), subpopulasi terpapar (E), dan subpopulasi terinfeksi (I). Selain itu, terdapat kompartemen (M) yang merepresentasikan jumlah pesan yang diberikan media tentang penyakit epidemi. Pada model diasumsikan individu yang terinfeksi dapat kembali menjadi individu rentan. Analisis dinamik yang dilakukan pada model meliputi penentuan titik kesetimbangan dan syarat eksistensinya, penentuan angka reproduksi dasar R0 dengan menggunakan matriks generasi selanjutnya serta analisis kestabilan. Berdasarkan hasil analisis diperoleh dua titik kesetimbangan model, yaitu titik kesetimbangan bebas penyakit dan titik kesetimbangan endemi. Titik kesetimbangan bebas penyakit selalu eksis sedangkan titik kesetimbangan endemi eksis dengan syarat tertentu. Titik kesetimbangan bebas penyakit bersifat stabil asimtotik lokal dan global ketika R0 < 1. Jenis kestabilan titik kesetimbangan endemi bergantung pada nilai R0, Rp, dan R01. Simulasi numerik dilakukan untuk mendukung hasil analisis dinamik yang diperoleh.
English Abstract
This final project discussed about dynamical analysis of SEIS epidemic model with the impact of media. In this model, the population is divided into three subpopulations, there are susceptible subpopulation (S), exposed subpopulation (E), and infected subpopulation (I). Beside that, there is compartement (M) that represents number of messages that the media gives about epidemic diseases (M). This model assumes that the infected individual can return to a susceptible individual. The dynamical analysis includes the determination of equilibrium points and existence conditions, determination of basic reproduction number R0 using next generation matrix and stability analysis. Based on the analysis results, two equilibrium points were obtained, namely the disease-free equilibrium point and endemic equilibrium point. The disease-free equilibrium point always exists while the endemic equilibrium point exists under certain conditions. The disease-free equilibrium point is a lokal and global asymptotically stable at R0 < 1. The stability type of an endemic equilibrium point depends on the value of R0, Rp, and R01. Numerical simulations were performed to support the result of the obtained dynamical analysis.
| Item Type: | Thesis (Sarjana) |
|---|---|
| Identification Number: | SKR/MIPA/2018/425/051809795 |
| Uncontrolled Keywords: | model epidemi SEIS, angka reproduksi dasar, fungsi Lyapunov, dampak media. SEIS epidemic model, basic reproduction number, Lyapunov function, impact of media. |
| Subjects: | 500 Natural sciences and mathematics > 515 Analysis > 515.3 Differential calculus and equations |
| Divisions: | Fakultas Matematika dan Ilmu Pengetahuan Alam > Matematika |
| Depositing User: | Budi Wahyono Wahyono |
| Date Deposited: | 12 Jun 2020 13:05 |
| Last Modified: | 18 Oct 2021 04:36 |
| URI: | http://repository.ub.ac.id/id/eprint/168774 |
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