KONTROL OPTIMAL MENGGUNAKAN PRINSIP MINIMUM PONTRYAGIN PADA MODEL PENYEBARAN PENYAKIT TUBERKULOSIS DI KALIMANTAN BARAT
DOI:
https://doi.org/10.25077/jmu.10.3.236-247.2021Abstract
Penyakit Tuberkulosis (TB) disebabkan karena bakteri mycrobacterium tuberculosis dan merupakan penyakit menular yang mempengaruhi paru-paru. Di Kalimantan Barat tercatat jumlah kasus baru TB sebanyak 3.463 kasus dengan angka insidens 70, 21 per 100.000 penduduk. Sedangkan dengan persentase kesembuhan 67, 5% pasien TB paru dinyatakan sembuh, dengan rincian dari 3611 pasien yang mendapatkan pengobatan, sebanyak 2436 pasien yang sembuh. Dengan pemberian vaksinasi dan pengobatan penularan penyakit TB dapat dicegah. Pada penelitian ini, model epidemi dibagi menjadi tiga subpopulasi, yaitu subpopulasi Susceptible (S), subpopulasi Infectious (I) dan subpopulasi Recovered (R). Dari ketiga subpopulasi tersebut kemudian dibentuk model epidemi tipe SIR. Untuk menekan penularan, sistem diberikan kontrol, yaitu vaksinasi (u1) pada bayi yang baru lahir dan kontrol pengobatan (u2) diberikan pada individu infective yang melakukan kontak langsung dengan individu susceptible. Tujuan pemberian kontrol tersebut adalah untuk mengurangi jumlah individu susceptible dan individu infective. Model epidemi SIR yang sudah diberikan kontrol (u1) dan (u2), diselesaikan dengan Prinsip Minimum Pontryagin untuk mendapatkan suatu kontrol optimal u ∗ 1 dan u ∗ 2 . Berdasarkan simulasi numerik yang telah dilakukan didapatkan hasil yaitu kontrol bekerja secara efektif dalam menekan penyebaran TB sehingga individu infective berkurang.
Kata Kunci: Tuberkulosis, Model SIR, Kontrol Optimal, Prinsip Minimum Pontryagin
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