Kontrol Optimal Model Dinamik Penyebaran Penyakit Tuberkulosis dengan Kekambuhan di Kota Semarang
DOI:
https://doi.org/10.12962/limits.v22i3.4349Keywords:
Tuberkulosis, Kekambuhan, Kontrol OptimalAbstract
Dalam penelitian ini, kami mengusulkan model dinamik SVIR (Susceptible, Vaccinated, Infectious, Recovered) dengan mempertimbangkan kekambuhan pada penyebaran penyakit Tuberkulosis (TB). Dalam model yang diusulkan ini, kami menggabungkan teori kontrol optimal yang bertujuan untuk mengurangi jumlah penyebaran kasus TB. Terdapat dua variabel kontrol yang digunakan, yaitu edukasi pencegahan TB kepada masyarakat umum, dan pengobatan untuk individu yang terinfeksi aktif. Dalam hal ini, untuk mencari solusi pengendalian yang optimal kami menggunakan Prinsip Minimum Pontryagin. Simulasi numerik dalam menyelesaikan sistem pada masalah kontrol optimal ini menggunakan metode numerik Sweep Maju-Mundur dan metode Runge-Kutta orde keempat. Hasil dari simulasi numerik digunakan untuk menggambarkan perbedaan antara strategi menggunakan kontrol dengan tanpa menggunakan kontrol. Dari hasil simulasi numerik, kami menemukan bahwa jika pengendalian edukasi pencegahan TB dan pengobatan diterapkan secara bersamaan akan lebih efektif dibandingkan dengan menerapkan kontrol secara terpisah, karena subpopulasi yang terinfeksi dapat dikendalikan dengan lebih baik di mana penurunan jumlah kasus mencapai 99.90% dan bertambahnya subpopulasi yang sembuh.
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