Kontrol Optimal Model Penanganan Stunting Di Provinsi Jawa Timur Menggunakan Prinsip Minimum Pontryagin

Antania, Yusvia (2025) Kontrol Optimal Model Penanganan Stunting Di Provinsi Jawa Timur Menggunakan Prinsip Minimum Pontryagin. Other thesis, Institut Teknologi Sepuluh Nopember.

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Abstract

Stunting adalah gangguan pertumbuhan kronis pada anak yang disebabkan oleh berbagai faktor, seperti kurangnya asupan gizi pada ibu, infeksi, pola konsumsi makanan yang tidak seimbang, serta kondisi sosial ekonomi yang rendah. Penyakit ini dapat berdampak jangka panjang terhadap kesehatan, perkembangan kognitif, dan produktivitas anak. Di Indonesia, prevalensi stunting masih melebihi standar WHO, termasuk di Provinsi Jawa Timur, yang meskipun mengalami penurunan dalam beberapa tahun terakhir, tetap menjadi masalah kesehatan utama. Pada Tugas Akhir ini akan dibahas mengenai model penanganan stunting yang terdiri atas lima sub-populasi, yaitu populasi balita rentan (Susceptible), populasi balita terpapar (Exposed), populasi balita stunting ringan (Infected-1), populasi balita stunting berat (Infected-2), dan populasi balita sembuh dari stunting (Recovered). Pada model tersebut ditambahkan kontrol berupa vaksinasi PD3I (u1) untuk populasi rentan dan pemberian nutrisi (u2) untuk populasi stunting ringan dan stunting berat. Dilakukan analisis sistem berupa analisis kestabilan di sekitar titik setimbang, analisis keteramatan, dan analisis keterkontrolan terlebih dahulu sebelum melakukan pengendalian. Penentuan kontrol optimal menggunakan Prinsip Minimum Pontryagin dengan tujuan untuk meminimalkan jumlah balita yang rentan mengalami stunting, serta balita yang mengalami stunting ringan maupun berat. Untuk simulasi numerik dilakukan dengan metode Runge-Kutta orde 4 pada Matlab. Setelah dilakukan analisis kestabilan, didapatkan bahwa pada titik kesetimbangan bebas penyakit dan titik kesetimbangan endemik, sistem bersifat tidak stabil. Sementara itu, analisis keteramatan dan keterkontrolan menunjukkan bahwa sistem bersifat teramati dan terkontrol. Berdasarkan hasil analisis dari permasalahan kontrol optimal dengan Prinsip Minimum Pontryagin serta simulasi menggunakan Runge Kutta orde 4 menunjukkan bahwa pemberian kontrol vaksinasi PD3I (u1) dan pemberian nutrisi (u2) sangat efektif dalam menurunkan jumlah individu yang engalami stunting ringan dan stunting berat.
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Stunting is a chronic growth disorder in children caused by various factors, such as lack of nutritional intake in mothers, infections, unbalanced food consumption patterns, and low socio-economic conditions. This disease can have long-term impacts on children’s health, cognitive development, and productivity. In Indonesia, the prevalence of stunting still exceeds WHO standards, including in East Java Province, which, although it has decreased in recent years, remains a major health problem. This Final Project will discuss the stunting handling model consisting of five sub-populations, namely the vulnerable toddler population (Susceptible), the exposed toddler population (Exposed), the mild stunting toddler population (Infected-1), the severe stunting toddler population (Infected-2), and the toddler population recovered from stunting (Recovered). In the model, control is added in the form of PD3I vaccination (u1) for the vulnerable population and nutrition (u2) for the mild and severe stunting populations. A system analysis is carried out in the form of stability analysis around the equilibrium point, observability analysis, and controllability analysis before carrying out control. Determination of optimal control using the Pontryagin Minimum Principle with the aim of minimizing the number of toddlers who are vulnerable to stunting, as well as those who have experienced mild or severe stunting. Numerical simulations are carried out using the 4th order Runge-Kutta method in Matlab. After the stability analysis, it was found that at the disease-free equilibrium point and the endemic equilibrium point, the system is unstable. Meanwhile, the observability and controllability analysis show that the system is observable and controlled. Based on the results of the analysis of the optimal control problem with the Pontryagin Minimum Principle and simulations using Runge Kutta order 4, it shows that providing PD3I vaccination control (u1) and providing nutrition (u2) is very effective in reducing the number of individuals experiencing mild and severe stunting.

Item Type:	Thesis (Other)
Uncontrolled Keywords:	Kontrol Optimal, Prinsip Minimum Pontryagin, Runge-Kutta orde empat, Stunting, Optimal Control, Pontryagin’s Minimum Principle, Fourth-order Runge Kutta, Stunting
Subjects:	Q Science > QA Mathematics > QA401 Mathematical models.
Divisions:	Faculty of Science and Data Analytics (SCIENTICS) > Mathematics > 44201-(S1) Undergraduate Thesis
Depositing User:	Yusvia Antania
Date Deposited:	25 Jul 2025 07:29
Last Modified:	25 Jul 2025 07:29
URI:	http://repository.its.ac.id/id/eprint/121536

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