Kontrol Optimal Upaya Pengobatan Penyakit Campak Menggunakan Model Endemi SIR

Abstract

Measles is an acute highly contagious disease caused by Paramyxovirus. Measles is considered as a dangerous disease because it cause complications, brain and other organs damage, lifelong disability, paralysis and even death. In the previous studies, it was known that the spread of measles highly dependent on number of infected individuals so it is necessary to control measles through treatment. In this paper, we study about the application of the optimal control theory on the system of differential equations of the SIR endemic model. Determination of the optimal control is obtained through the application of the Pontryagin minimum principle. The main target in this paper is to find a unique optimal control where the optimal control can be described as an efficiency rate of treatment in individuals infected with measles to decrease the number of infected individuals.