Maximum Principle for Optimal Control of COVID-19 Spread

Abstract

Covid-19 is a disease caused by a new corona virus that has spread throughout the world and become a pandemic. It is classified as an infectious disease that can be transmitted from human to human through droplets. So that we need controls to reduce the spread of Covid-19. The optimal control that will be carried out this work is self-precaution, treatment and quarantined that will be applied to the dynamical modelling of Covid-19 spread using the Pontryagin’s Maximum Principle (PMP) to find out the optimal solution for the control. According to this principle the optimal control, corresponding optimal state, and adjoint function must minimize the Hamiltonian function. PMP converts the optimal control problem into a multipoint boundary value problem. That is, the optimality condition results in control. The optimal control variable, corresponding state and adjoint can be computed by solving an Ordinary Differential Equation system. The control strategies is aimed to reduce covid-19 transmission. Numerical results show the effectiveness of the control strategies in reducing Covid-19 spread. It is found that self-precaution more effective than treatment and quarantined.