Pengendalian Optimal dan Analisis Model Penyebaran Penyakit Pneumonia pada Balita di Provinsi Jawa Timur Menggunakan Prinsip Minimum Pontryagin

Syahputri, Denisa Dwi (2024) Pengendalian Optimal dan Analisis Model Penyebaran Penyakit Pneumonia pada Balita di Provinsi Jawa Timur Menggunakan Prinsip Minimum Pontryagin. Other thesis, Institut Teknologi Sepuluh Nopember.

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Abstract

Pneumonia merupakan jenis penyakit saluran pernapasan akut yang menyerang paru-paru. Adapun mikroorganisme penyebab penyakit pneumonia, diantaranya virus, bakteri, parasit,
paparan bahan kimia, jamur, atau kerusakan fisik pada paru-paru. Pneumonia termasuk dalam daftar 10 penyakit dengan jumlah kasus terbanyak menurut laporan Kementerian Kesehatan RI pada April 2023. Pneumonia menjadi penyebab kematian terbesar pada balita kelompok usia 12-59 bulan, yakni mencapai 12,5 persen. Pada Tugas Akhir ini akan dibahas mengenai model penyebaran penyakit pneumonia yang terdiri atas 5 populasi yaitu populasi rentan (Susceptible), populasi terpapar (Exposed), populasi terinfeksi pneumonia ringan (Infected-1), populasi terinfeksi pneumonia berat (Infected-2), dan populasi sembuh (Recovered). Pada model tersebut ditambahkan kontrol berupa pengobatan tahap pertama (u1) untuk populasi terinfeksi pneumonia ringan dan pengobatan tahap kedua (u2) untuk populasi terinfeksi pneumonia berat. Perlu dilakukan analisis kestabilan di sekitar titik setimbang dan analisis keterkontrolan terlebih dahulu sebelum melakukan pengendalian. Penentuan kontrol optimal menggunakan Prinsip Minimum Pontryagin dengan tujuan untuk meminimumkan populasi terpapar, populasi terinfeksi pneumonia ringan, dan populasi terinfeksi pneumonia berat. Untuk simulasi numerik dilakukan dengan metode Runge-Kutta orde empat pada Matlab. Setelah dilakukan analisis kestabilan, didapatkan bahwa pada titik kesetimbangan bebas penyakit dan titik kesetimbangan endemik, sistem bersifat stabil. Berdasarkan analisis keterkontrolan diperoleh bahwa sistem bersifat terkontrol sehingga sistem dapat dikendalikan. Berdasarkan hasil analisis dari permasalahan kontrol optimal dengan Prinsip Minimum Pontryagin serta simulasi menggunakan Runge Kutta orde 4 menunjukkan bahwa pemberian kontrol pengobatan tahap pertama (u1) dan pengobatan tahap kedua (u2) sangat efektif dalam menurunkan jumlah individu terinfeksi pneumonia ringan dan pneumonia berat.
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Pneumonia is a type of acute respiratory disease that attacks the lungs. The microorganisms that cause pneumonia include viruses, bacteria, parasites, exposure to chemicals, fungi, or physical damage to the lungs. Pneumonia is included in the list of 10 diseases with the highest number of cases according to the Indonesian Ministry of Health report in April 2023. Pneumonia is the biggest cause of death in toddlers aged 12-59 months, reaching 12,5 percent. In this final assignment, we will discuss the model for the spread of pneumonia which consists of 5 subpopulations, namely the susceptible population (Susceptible), the exposed population (Exposed), the population infected with mild pneumonia (Infected-1), the population infected with severe pneumonia (Infected-2), and recovered population (Recovered). In this model, controls are added in the form of first stage treatment (u1) for the population infected with mild pneumonia and second stage treatment (u2) for the population infected with severe pneumonia. It is necessary to carry out a stability analysis around the equilibrium point and a controllability analysis first before carrying out control. Optimal control is determined by Pontryagin's Minimum Principle with the aim of minimizing the exposed population, the population infected with mild pneumonia, and the population infected with severe pneumonia. Numerical simulation can be carried out using the fourth order Runge-Kutta method in Matlab. After carrying out a stability analysis, it was found that at the disease-free equilibrium point and the endemic equilibrium point, the system was stable. Based on controllability analysis, it is found that the system is controlled so that the system can be controlled. Based on the results of the analysis of the optimal control problem with Pontryagin's Minimum Principle simulated with Runge Kutta order 4, it shows that the first stage of treatment control (u1) and the second stage of treatment (u2) are very effective in reducing the number of individuals infected with mild pneumonia and severe pneumonia.

Item Type:	Thesis (Other)
Uncontrolled Keywords:	kestabilan, kontrol optimal, pneumonia, prinsip minimum pontryagin, stability, optimal control, pneumonia, minimum pontryagin principle
Subjects:	Q Science > QA Mathematics Q Science > QA Mathematics > QA372.B9 Differential equations--Numerical solutions. Runge-Kutta formulas--Data processing. Q Science > QA Mathematics > QA401 Mathematical models.
Divisions:	Faculty of Mathematics and Science > Mathematics > 44201-(S1) Undergraduate Thesis
Depositing User:	Denisa Dwi Syahputri
Date Deposited:	06 Aug 2024 18:49
Last Modified:	06 Aug 2024 18:49
URI:	http://repository.its.ac.id/id/eprint/113908

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