MASALAH KONTROL OPTIMAL PADA PENYEBARAN COVID-19 DI JAWA TENGAH DENGAN VAKSINASI
DOI:
https://doi.org/10.25077/jmu.10.4.538-552.2021Abstract
COVID-19 merupakan penyakit menular yang disebabkan oleh Severe Acute Respiratory Syndrome Coronavirus-2 (SARS-Cov-2) yang menyebar hampir ke suluruh penjuru dunia. Pada penelitian ini disusun model epidemik SIVR untuk mengetahui penyebaran COVID-19 dengan menggunakan teori kontrol optimal. Model epidemik SIVR merupakan salah satu pemodelan matematika yang mendeskripsikan interaksi antara populasi rentan, terinfeksi, tervaksin dan populasi yang sembuh. Kontrol dalam penelitian ini bertujuan untuk meminimalkan jumlah populasi terinfeksi agar dapat menekan kasus penyebaran COVID-19. Simulasi pada penelitian ini ditinjau dari dua keadaan R0 (Bilangan Reproduksi Dasar) , dengan R0 > 1 untuk kasus terjadinya endemik dan R0 < 1 untuk kasus terjadinya bebas penyakit. Berdasarkan solusi numerik model epidemik SIVR dengan dan tanpa pengontrol menggunakan Prinsip Maksimum Pontryagin metode Runge-Kutta orde 4, diperoleh hasil bahwa semakin tinggi jumlah populasi tervaksin COVID-19 menyebabkan jumlah populasi rentan semakin berkurang, begitupun sebaliknya, yang berarti bahwa vaksin dapat menekan kasus penyebaran COVID-19 di Jawa Tengah.
Kata Kunci: Model epidemik, COVID-19, vaksinasi, kestabilan, kontrol optimal
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