Pramono, Rochman Dwito (2021) Analisis Kestabilan dan Kontrol Optimal Model Penyebaran Penyakit Covid-19 Antar Kota Surabaya dan Sidoarjo dengan Vaksinasi. Undergraduate thesis, Institut Teknologi Sepuluh Nopember.
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Abstract
Wabah Covid-19 merupakan penyakit menular yang mewabah karena disebabkan oleh Coronavirus. Hingga saat ini permasalahan penyebaran Covid-19 masih menjadi bahan penelitian. Secara umum, model penyebaran penyakit yang digunakan terdiri dari Susceptible, Exposed, Infected, dan Recovered. Pada penelitian ini membahas tentang penyebaran Covid-19 antar dua kota berdekatan yaitu kota Surabaya dan kota Sidoarjo. Untuk mencegah penyebaran penyakit, sistem diberi kontrol berupa vaksinasi pada individu yang rentan. Fokus dalam penelitian ini membahas tentang analisis pada model penyebaran Covid-19 dengan menganalisis kestabilan dengan menggunakan kriteria Routh Hurwitz. Kontrol optimal dilakukan dengan menggunakan Prinsip Minimum Pontryagin dengan menggunakan kontrol vaksinasi pada kota Surabaya dan kota Sidoarjo. Solusi numerik dilakukan dengan metode Runge Kutta orde empat, dan simulasi menggunakan MATLAB. Hasil analisis menunjukan tidak stabil pada kriteria Routh Hurwitz karena terdapat perubahan tanda pada kolom pertama pada tabel Routh. Dan pada simulasi menunjukan adanya penurunan tingkat penyebaran penyakit Covid-19 setelah pemberian kontrol.
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Pandemic outbreak of Covid-19 is an infectious disease which is caused by the Coronavirus. The disease spread model is generally used which consists of Susceptible, Exposed, Infected, and Recovered. This study discusses the spread of the disease between two neighbor cities, namely the city of Surabaya and the city of Sidoarjo. There are eight similarities equations used. To prevent the spread of the disease, the system is controlled in the form of vaccination of susceptible individuals. This final project focusses on the analysis of the model by analyzing the stability using the Routh Hurwitz criteria. The optimal control was carried out using the Pontryagin’s Principle with using vaccination control in the city of Surabaya and the city of Sidoarjo. The fourth-order Runge Kutta method is used as the numerical solution and the simulation is carried out with MATLAB. The results of the analysis shows that there is unstable in the Routh Hurwitz criteria because there is a change in the sign in the first column on the routh table. And the simulation shows a reduces the spread of Covid-19 disease after giving control.
| Item Type: | Thesis (Undergraduate) |
|---|---|
| Uncontrolled Keywords: | Model Covid-19, Kestabilan, Kontrol Optimal, Prinsip Minimum Pontryagin, Metode Runge-Kutta ============================================================ Covid-19 Model, Stability, Optimal Control, Pontryagin Minimum Principle, Runge-Kutta Method |
| Subjects: | Q Science > QA Mathematics > QA372.B9 Differential equations--Numerical solutions. Runge-Kutta formulas--Data processing. |
| Divisions: | Faculty of Science and Data Analytics (SCIENTICS) > Mathematics > 44201-(S1) Undergraduate Thesis |
| Depositing User: | Rochman Dwito Pramono |
| Date Deposited: | 27 Aug 2021 05:42 |
| Last Modified: | 20 Dec 2024 08:27 |
| URI: | http://repository.its.ac.id/id/eprint/90061 |
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