Astuti, SyivaFindi (2013) Analisis Dinamik Model Epidemik Sir Dengan Kernel Tundaan Dan Laju Infeksi Tersaturasi. Sarjana thesis, Universitas Brawijaya.
Abstract
Pada skripsi ini dibahas model epidemik SIR dengan kernel tundaan, variabel informasi dan laju infeksi tersaturasi, dimana individu rentan diasumsikan memenuhi persamaan logistik dan laju kejadian adalah bentuk tersaturasi. Eksistensi dan kestabilan lokal titik kesetimbangan ditentukan dan dipengaruhi oleh bilangan reproduksi dasar . Terdapat dua titik kesetimbangan, yaitu titik kesetimbangan bebas penyakit yang stabil bila angka reproduksi dasar kurang dari satu, dan titik kesetimbangan endemik yang stabil bila angka reproduksi dasar lebih dari satu. Model ini mengalami dua bifurkasi yaitu bifurkasi transkritikal dan bifurkasi Hopf. Selanjutnya simulasi numerik diberikan untuk mengilustrasikan hasil analisis.
English Abstract
The final project discusses a SIR epidemic model with time delay, information variable and saturated incidence rate, where the susceptibles are assumed to satisfy the logistic equation and the incidence term, in the saturated form of susceptible. Existence and local stability of equilibrium points are determined by basic reproduction number . There are two equilibrium points, namely free disease equilibrium point, which is stable if the basic reproduction number less than one, and the endemic equilibrium point,which is stable if the basic reproduction number is greater than one. This model exhibits two bifurcations, namely transcritical bifurcation and Hopf bifurcation. Numerical simulations are carried out to explain the analytycal results.
| Item Type: | Thesis (Sarjana) |
|---|---|
| Identification Number: | SKR/MIPA/2013/286/051307815 |
| Subjects: | 500 Natural sciences and mathematics > 510 Mathematics |
| Divisions: | Fakultas Matematika dan Ilmu Pengetahuan Alam > Matematika |
| Depositing User: | Hasbi |
| Date Deposited: | 05 Sep 2013 09:20 |
| Last Modified: | 25 Oct 2021 02:27 |
| URI: | http://repository.ub.ac.id/id/eprint/153544 |
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