Aditya, Fajar (2014) Analisis Dinamik Model Sirs Dengan Transport-Related Infection. Sarjana thesis, Universitas Brawijaya.
Abstract
Pada skripsi ini dibahas model matematika tipe SIRS (Susceptible Infective Removed) yang menggambarkan penyebaran penyakit menular melalui transportasi antar-dua wilayah dengan transport-related infection. Pembahasan skripsi ini terdiri dari penentuan titik kesetimbangan, syarat eksistensi titik kesetimbangan, dan analisis kestabilan titik kesetimbangan . Eksistensi dan kestabilan titik kesetimbangan ditentukan oleh angka reproduksi dasar yang ditentukan dengan menggunakan metode generasi selanjutnya. Berdasarkan hasil analisis diperoleh bahwa, jika angka reproduksi dasar lebih besar dari satu, maka titik kesetimbangan endemi stabil, sedangkan jika angka reproduksi kurang dari atau sama dengan satu, maka titik kesetimbangan bebas penyakit stabil. Pada bagian akhir disimulasikan hasil yang telah diperoleh secara numerik.
English Abstract
This final project discusses a SIRS model, (Susceptible Infective Removed) which describes the spread of an infectious disease through transportation between two regions using trnasport-related infection. Determination of equilibrium points, existence condition for equilibrium points and stability analysis of equilibrium points are discussed in this final object. Existence and stability of equilibrium point are marked by basic reproduction number which is determined by using next generation method. According to the analysis result that if the reproduction number is greater then one, the endemic equilibrium point is stable, and if the reproduction number is less than or equal one, the disease-free equilibrium point is stable. Finally, the result of dynamical analysis are simulated numerically.
| Item Type: | Thesis (Sarjana) |
|---|---|
| Identification Number: | SKR/MIPA/2014/382/051406895 |
| Subjects: | 500 Natural sciences and mathematics > 510 Mathematics |
| Divisions: | Fakultas Matematika dan Ilmu Pengetahuan Alam > Matematika |
| Depositing User: | Budi Wahyono Wahyono |
| Date Deposited: | 04 Nov 2014 14:31 |
| Last Modified: | 21 Oct 2021 06:28 |
| URI: | http://repository.ub.ac.id/id/eprint/154021 |
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COVER.pdf Download (1MB) | Preview |
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BAB_III_(Repaired)&_Bab_4.pdf Download (2MB) | Preview |
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DAFTAR_PUSTAKA_REVISI.pdf Download (1MB) | Preview |
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KATA_PENGANTAR.pdf Download (1MB) | Preview |
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BAB_1_N_2.pdf Download (2MB) | Preview |
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DAFTAR_ISI_REVISI2.pdf Download (1MB) | Preview |
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LAMPIRANFIX.pdf Download (1MB) | Preview |
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LEMBAR_PERNYATAAN_REVISI.pdf Download (1MB) | Preview |
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ABSTRAK_REVISI.pdf Download (1MB) | Preview |
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