Asih, Putri Lestari (2020) Analisis Dinamik Model Epidemi Pneumonia dengan Pengobatan. Sarjana thesis, Universitas Brawijaya.
Abstract
Pada skripsi ini dibahas analisis dinamik model epidemi pneumonia dengan pengobatan. Model ini memiliki empat subpopulasi, yaitu subpopulasi rentan pneumonia (
English Abstract
This final project discusses about dynamical analysis of pneumonia epidemic model with treatment. In this model, the population is divided into four subpopulations, namely susceptible subpopulations who are at risk of acquire pneumonia infection (S), subpopulation who carry the pneumonia bacteria (C), subpopulation who infected by pneumonia (I), and subpopulation who recovered after getting pneumonia treatment (R). Dynamical analysis is performed by finding the equilibrium points, the basic reproduction number (ℛ0) and analizing the local and global stability of equilibrium. Dynamical analysis show that the model has two equilibrium points, namely the disease free equilibrium point and the endemic equilibrium point. The disease free equilibrium point always exist, while the endemic equilibrium point exist with certain conditions. The disease free equilibrium point is locally asymptotically without condition and is globally asymptotically stable when ℛ0<1, but the endemic equilibrium point is locally asymptotically stable if it satisfies Routh-Hurwitz criteria and is globally asymptotically stable with certain conditions. Numerical simulations shows the same result with dynamical analysis.
Other obstract
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| Item Type: | Thesis (Sarjana) |
|---|---|
| Identification Number: | 0520090204 |
| Uncontrolled Keywords: | pneumonia, titik kesetimbangan, angka reproduksi dasar, kestabilan lokal, kestabilan global |
| Subjects: | 500 Natural sciences and mathematics > 515 Analysis > 515.3 Differential calculus and equations > 515.39 Dynamical systems |
| Divisions: | Fakultas Matematika dan Ilmu Pengetahuan Alam > Matematika |
| Depositing User: | ismanto |
| Date Deposited: | 15 Feb 2021 01:01 |
| Last Modified: | 11 Apr 2023 01:31 |
| URI: | http://repository.ub.ac.id/id/eprint/183067 |
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Text (DALAM MASA EMBARGO)
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