Husadaningsih, Tyas (2018) Analisis Dinamik Model Penyebaran Penyakit Kolera Dengan Karantina. Magister thesis, Universitas Brawijaya.
Abstract
Pada tesis ini dibahas analisis dinamik model penyebaran penyakit kolera dengan karantina. Model dikonstruksi dengan mempertimbangkan kontak populasi manusia rentan dengan populasi manusia terinfeksi serta laju pembasmian bakteri. Hal ini dilakukan karena penyakit kolera dapat menular antar manusia, sedangkan pembasmian bakteri mengakibatkan jumlah populasi bakteri berkurang. Terdapat lima populasi dalam model, yaitu populasi manusia rentan, populasi manusia terinfeksi, populasi manusia dikarantina, populasi manusia sembuh, dan populasi bakteri. Analisis dinamik dilakukan dengan menentukan titik kesetimbangan beserta syarat eksistensinya dan menganalisis kestabilan lokal titik kesetimbangan tersebut. Selain itu, dilakukan pula simulasi numerik untuk mengilustrasikan hasil analisis. Berdasarkan hasil analisis, terdapat dua titik kesetimbangan, yaitu titik kesetimbangan bebas infeksi yang selalu eksis dan titik kesetimbangan endemik yang eksis dengan syarat tertentu. Titik kesetimbangan bebas infeksi bersifat stabil asimtotik lokal apabila memenuhi syarat
English Abstract
This thesis discusses a dynamical analysis of model of cholera disease spread with quarantine. The model is constructed by considering contact betwen susceptible human populations with infected human populations and the rate of bacterial eradication. This is done because cholera diseases can spread among humans, while the eradication of bacteria resulted in reduced bacterial population. There are five populations in the model: the susceptible human population, the infected human population, the quarantined human population, the recovered human population, and the bacterial population. The conducted dynamical analysis consists of determination of equilibrium point and their existence conditions, followed by local stability analysis on case equilibrium point. Analytical result shows that there are two equilibria, namely disease free equilibrium, which always exists and the endemic equilibrium, which needs a certain condition to exist. The disease free equilibrium point is local asymptotically stable if the basic reproduction number
| Item Type: | Thesis (Magister) |
|---|---|
| Identification Number: | TES/515.39/HUS/a/2018/041802369 |
| Uncontrolled Keywords: | DYNAMICS, STRUCTURAL DYNAMICS, CHOLERA - EPIDEMIOLOGY, QUARANTINE |
| Subjects: | 500 Natural sciences and mathematics > 515 Analysis > 515.3 Differential calculus and equations > 515.39 Dynamical systems |
| Divisions: | S2/S3 > Magister Matematika, Fakultas MIPA |
| Depositing User: | Nur Cholis |
| Date Deposited: | 25 Apr 2018 02:02 |
| Last Modified: | 21 Oct 2021 07:32 |
| URI: | http://repository.ub.ac.id/id/eprint/9857 |
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