An optimal control of prevention and treatment of COVID-19 spread in Indonesia

Abstract

In this paper we analyze COVID-19 spread in Indonesia using an epidemio logical model. We consider symptomatic and asymptomatic infections in the model. We analyze the equilibria of the model and their stability which depend on the basic reproduction ratio for symptomatic and asymptomatic infections. Furthermore, we use optimal control in prevention and treatment in decreasing the number of positive COVID-19 patients in Indonesia. Furthermore, we analyze the existence of optimal control using the Pontryagin minimum principle. We also give numerical simulation of COVID-19 spread with and without the control.  According to the simulation, COVID-19 spread could be reduced by using prevention and treatment control simultaneously.