APLIKASI PERSAMAAN DIFERENSIAL STOKASTIK PADA MASALAH KONTROL OPTIMUM BERKENDALA
Abstract
Penyebaran virus Covid-19 adalah salah satu fenomena yang dapat dimodelkan. Pada penelitian ini dibahas tentang kontrol optimal pada model stokastik dari penyebaran virus Covid 19 yang terdiri atas tiga populasi yaitu rentan (Susceptible), Terinfeksi (Infected) dan pulih (Recovered). Adanya kondisi fisik yang berbeda tiap individu dan perubahan perilaku dari individu menjadi alasan penyusunan model stokastik ini. Pada penelitian ini model penyebaran virus Covid-19 diasumsikan dapat dikendalikan oleh pemerintah dengan pemberian kontrol vaksinasi dan isolasi dengan tujuan meminimalkan jumlah individu terinfeksi dan biaya vaksinasi. Model dikonstruksikan berdasarkan 2 kasus yaitu Model I adalah model dengan vaksinasi dan model II adalah model dengan isolasi. Kedua model tersebut akan dianalisis dengan menerapkan Prinsip Stokastik Maksimum. Prinsip ini dilakukan terhadap Hamiltonian dari persamaan optimal yang terbentuk untuk menentukan kontrol optimalnya.
Kata Kunci : Covid-19, Vaksinasi, Isolasi, Hamiltonian, Prinsip Stokastik Maksimum.
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