MODEL ANALYSIS AND OPTIMAL CONTROL OF THE SPREAD OF COVID-19 TRANSMISSION DYNAMICS IN CENTRAL JAVA PROVINCE, INDONESIA

Abstract

COVID-19 is currently a pandemic that is considered as the biggest global threat that classified as the human-to-human transmissionable disease. This final project is discussed the model for the spread of COVID-19 also analyzed the stability of the model and optimal control. The local stability of the system around the equilibrium point is determined by the Routh-Hurwitz stability criteria.So that from the model, two equilibrium points are obtained. That is the disease-free equilibrium point and the endemic equilibrium point. The disease-free equilibrium point is asymptotically stable if the basic reproduction number is less than one and the endemic equilibrium point is asymptotically stable if the basic reproduction number is more than one. There are three control variables that used for optimal control, they are self prevention, medication, and self quarantined. In determining the form of optimal control to minimize the number of infected individuals and the associated costs, this project used Pontryagin's Maximum Principle. The results of numerical simulations that is completed by the Runge Kutta Order-4 method prove that by using all the three control variables in minimizing the infected individuals and maximizing the recovered individuals is effective. Keywords : COVID-19, Routh-Hurwitz, Optimal Control, Pontryagin's Maximum Principle, Runge Kutta Orde-4.