Optimal control on model of COVID-19 with ineffective vaccination and quarantine

Abstract

In this paper, we present an optimal control approach for an (SEIRV) epidemic model of COVID-19 disease by controlling quarantine measures on susceptible individuals and controlling the vaccination rate for susceptible individuals, exposed but not yet infectious individuals, and asymptomatic infectious individuals to reduce the disease burden and related costs. We have proven that an optimal control does exist, and we used Pontryagin’s maximum principle to characterize the optimal control. In numerical simulations, we solve the optimal control problem by the fourth-order Runge–Kutta method. Moreover, we discuss different cases for optimal control of quarantine measures and vaccination quantity presented through graphical representations.