Putri, Nadhira Azane (2020) Desain Kendali Optimal Pada Model Penyebaran Penyakit Malaria Dengan Menggunakan Prinsip Minimum Pontryagin. Other thesis, Institut Teknologi Sepuluh Nopember.
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Abstract
Malaria merupakan masalah utama untuk kesehatan di
Indonesia, terutama di Provinsi Papua yang mempunyai jumlah
penderita terbesar untuk penyakit malaria. Oleh karena itu,
dilakukan desain kendali penyebaran penyakit malaria di Provinsi
Papua Indonesia. Pada tugas akhir ini, dijelaskan tentang kendali
optimal pada model matematika penyebaran malaria dilengkapi
dengan tiga variabel kendali yaitu pencegahan manusia,
pengobatan manusia dan penyemprotan insektisida terhadap
nyamuk untuk mengurangi banyaknya manusia yang terinfeksi.
Kemudian dilakukan perancangan masalah kendali optimal
dengan menggunakan metode Prinsip Minimum Pontryagin untuk
menurunkan sistem persamaan diferensial sebagai kondisi yang
harus dipenuhi variabel-variabel kendali optimum. Selanjutnya
metode Runge-Kutta orde 4 digunakan untuk menyelesaikan
sistem persamaan secara numerik dengan bantuan software
SCILAB 6.0. Hasil simulasi numerik menunjukkan menurunnya
populasi manusia yang terinfeksi Parasit Plasmodium setelah
adanya pemberian kendali berupa pengobatan dengan presentase
reduksi sebesar 99.5% selama 100 hari
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Malaria is a major problem for health in Indonesia,
especially in Papua Province which has the largest number of
sufferers for malaria. Therefore, the control of malaria spread in
the Papua Province of Indonesia was carried out. In this final
project, the optimal control in the mathematical model of malaria
spread is explained with three control variables namely human
prevention, human treatment and spraying of insecticides on
mosquitoes to reduce the number of infected humans. Then do the
optimal control problem design using Pontryagin's Minimum
Principle method to derive the system of differential equations as
a condition that must be satisfied by the optimum control
variables. Furthermore, the Runge-Kutta 4th-order method is
used to solve the numerical equation system with the help of
SCILAB 6.0 software. The results of numerical simulation show a
decrease in the human population infected with Plasmodium
parasites after providing controls in the form of treatment with a
reduction precentage of 99,5% for 100 days
| Item Type: | Thesis (Other) |
|---|---|
| Uncontrolled Keywords: | Malaria, Kendali Optimal, Prinsip Minimum Pontryagin, Runge-kutta |
| Subjects: | Q Science Q Science > Q Science (General) > Q180.55.M38 Mathematical models 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: | Nadhira Azane Putri |
| Date Deposited: | 19 Aug 2020 04:27 |
| Last Modified: | 12 Jun 2023 06:40 |
| URI: | http://repository.its.ac.id/id/eprint/79176 |
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