KONTROL OPTIMAL PADA MODEL EPIDEMIK PENYAKIT DEMAM BERDARAH DENGUE DI PROVINSI NUSA TENGGARA BARAT

Abstract

Dengue haemorrhagic fever (DHF) is one of the dangerous and high-risk diseases in Indonesia. West Nusa Tenggara Province is one of the regions in Indonesia that is often reported to have a high number of DHF cases. In this research, SIR-SI disease transmission model of DHF is constructed with control in the form of the 3M program and treatment. The purpose of this research is to minimize the number of infected individuals and minimize the cost of control provided. The method used in this research is Pontryagin's minimum principle to determine the optimal control and forward-backward fourth order Runge-Kutta method to obtain the numerical solution. Based on the results and simulations research that has been conducted, it was obtained that the system is unstable at disease-free equilibrium point and asymptotically stable at endemic equilibrium point. Furthermore, with the implementation of control such as the 3M program and treatment effectively minimize the number of infected individuals while keeping the cost of control provided for 90 days.