Dewi, Nihaya Alivia Coraima (2018) Optimasi Domain of Attraction Model Epidemik Pada Dua Wilayah dengan Tiga Lintasan. Masters thesis, Institut Teknologi Sepuluh Nopember.
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Abstract
Banyaknya individu yang bepergian dari suatu wilayah menuju wilayah lain melewati berbagai lintasan memungkinkan adanya penularan penyakit dari individu terinfeksi kepada individu yang rentan. Pada penelitian ini dikonstruksi model matematika tipe SEITR (Susceptible Exposed Infected Treatment Removed) untuk menggambarkan penyebaran penyakit menular antar dua wilayah dengan tiga-lintasan. Model dikonstruksi dengan adanya individu yang bepergian antar dua wilayah dengan tiga-lintasan
bercabang dan terdapat pengobatan pada populasi individu yang teinfeksi, sehingga menghasilkan populasi baru yaitu populasi treatment. Selanjutnya dilakukan analisis penyebaran virus dengan melakukan analisis kestabilan
serta melakukan simulasi numerik, dan mencari domain of attraction untuk mengetahui daerah penyebaran penyakit, serta dilakukan optimasi domain untuk mengetahui pusat penyebaran yang selanjutnya dapat diberikan saran terhadap daerah tersebut untuk dilakukan isolasi. Berdasarkan hasil analisis kestabilan diperoleh sistem tidak stabil jika rate transmisi penyakit lebih besar daripada rate pengobatan, dan berdasarkan analisis domain of attraction diperoleh hasil bahwa sumber penyebaran penyakit terletak pada daerah yang mempunyai rate transmisi yang lebih besar.
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The number of individuals traveling from an area towards the other regions passed through a variety of pathways allows the transmission of disease from the infected individual vulnerable to individuals. On the research of
mathematical model was constructed type SEITR (Susceptible Exposed Infected Treatment Removed) for describe the spread of infectious diseases between the
two regions with the three-path. The model constructed by the presence of individuals who travel between the two territories with three-path branched and there is treatment in a population of individuals infected birds, resulting in new population population treatment. Further analysis of the spread of the virus is done by performing an analysis of the stability and numerical simulation, and look for the domain of attraction to �nd out the area of the spread of disease, as well as domain optimization done for knowing the next distribution centre can be given suggestions towards the area to do isolation. Based on the stability analysis results, the system is unstable if the transmission rate of the disease is greater than the treatment rate, and based on the domain of attraction analysis, it is found that the source of the disease spread lies in the region having higher transmission rate.
| Item Type: | Thesis (Masters) |
|---|---|
| Uncontrolled Keywords: | Model Tiga Lintasan, Kestabilan, Domain of Attraction |
| Subjects: | Q Science > QA Mathematics > QA402 System analysis. |
| Divisions: | Faculty of Mathematics, Computation, and Data Science > Mathematics > 44101-(S2) Master Thesis |
| Depositing User: | Nihaya Alivia Coraima Dewi |
| Date Deposited: | 09 Aug 2021 21:44 |
| Last Modified: | 23 Apr 2024 03:12 |
| URI: | http://repository.its.ac.id/id/eprint/58509 |
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