Kontrol Optimal Penyebaran Penyakit Demam Berdarah Dengan Pengaruh Penyemprotan Insektisida Dan Pengobatan

Al Aziim, Sulthon Amar (2021) Kontrol Optimal Penyebaran Penyakit Demam Berdarah Dengan Pengaruh Penyemprotan Insektisida Dan Pengobatan. Undergraduate thesis, Institut Teknologi Sepuluh Nopember.

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Abstract

Demam berdarah adalah salah satu masalah kesehatan yang utama pada beberapa provinsi di Indonesia, salah satunya adalah provinsi Sulawesi Selatan. Penyebaran penyakit demam berdarah akan meningkat ketika musim hujan dikarenakan nyamuk Aedes Aegypti sebagai vektor penyebaran penyakit utamanya akan bertelur dan menetaskan telurnya pada genangan air sehingga menjadi jentik larva. Sebelumnya telah dilakukan penelitian mengenai model dan analisa penyebaran penyakit demam berdarah di Sulawesi Selatan. Sehingga dilakukan pengendalian penyebaran penyakit demam berdarah dengan pemberian kontrol berupa penyemprotan insektisida dan pengobatan dengan tujuan mengurangi populasi manusia yang terinfeksi. Pada Tugas Akhir ini dibahas mengenai model penyebaran penyakit demam berdarah dengan kontrol, titik kesetimbangan bebas penyakit dan endemik, dan analisa sifat model. Kemudian dilakukan penyelesaian kontrol optimal dengan menggunakan metode Prinsip Minimum Pontryagin. Selanjutnya dilakukan penyelesaian solusi numerik dengan metode Runge Kutta orde empat dengan bantuan software MATLAB. Berdasarkan hasil analisis dan hasil simulasi menunjukkan bahwa sistem stabil asimtotik pada titik kesetimbangan endemik dan titik kesetimbangan bebas penyakit, dan didapatkan menurunnya populasi manusia yang terinfeksi penyakit demam berdarah dengan adanya pemberian kontrol berupa penyemprotan insektisida dan pengobatan dengan persentase penurunan sebesar 99% selama 12 bulan. ==================================================================================================== Dengue fever is one of the main health problems in several provinces in Indonesia, one of which is the province of South Sulawesi. The spread of dengue fever will increase during the rainy season because the Aedes Aegypti mosquito as the main distribution vector will lay eggs and incubate their eggs in puddles so that they become larvae. Previously, research on the model and analysis of the spread of dengue fever has been carried out in South Sulawesi.Therefore, optimal control of the spread of dengue fever was carried out by providing control in the form of spraying insecticides and treatment with the purpose of reducing the infected human population. This Final Project discusses the distribution model of dengue fever with control, disease-free and endemic equilibrium points, and stability analysis of the model. Then the optimal control solution is carried out using the Pontryagin Minimum Principle method. Next, the numerical solution was solved using the fourth-order Runge Kutta method with the help of MATLAB software. Based on the results of the analysis and simulation results indicate that the system is asymptotically stable at the endemic equilibrium point and the equilibrium point is free of disease, and it was found that the human population infected with dengue fever was decreasing with the provision of control in the form of insecticide spraying and treatment with a percentage reduction of 99% for 12 months.

Item Type: Thesis (Undergraduate)
Uncontrolled Keywords: Demam Berdarah, Model Matematika, Kontrol Optimal, Runge Kutta, Dengue Fever, Mathematics Model, Optimal Control, Runge Kutta
Subjects: 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.
R Medicine > RC Internal medicine > RC137 Dengue
Divisions: Faculty of Science and Data Analytics (SCIENTICS) > Mathematics > 44201-(S1) Undergraduate Thesis
Depositing User: Sulthon Amar Al Aziim
Date Deposited: 25 Aug 2021 09:19
Last Modified: 25 Aug 2021 09:19
URI: https://repository.its.ac.id/id/eprint/89731

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