Application of optimal control on mathematical model for spreading of Covid-19

Corona virus (SARS-CoV-2) is a collection of viruses that infect the respiratory system. The disease caused by infection with this virus is called Covid-19 which can cause mild disturbances to the respiratory system and can cause death. The SEQIJR epidemic model (Susceptible, Exposed, Quarantine, Infectious not hospital, Hospitalized Infectious, Recovered) was studied by adding control variables to analyze the dynamics of the spread of Covid-19. Optimal control strategy is applied to minimize the number of infected individuals, with controls in the form of awareness campaign, quarantine and isolation. In the mathematical model of the spread of Covid-19, there are many unknown parameters, so the genetic algorithm method is used to estimate the parameters of the Covid-19 spread model. To reduce the spread of Covid-19, an optimal control design is applied using the Pontryagin minimum principle. Furthermore, it is simulated numerically with the forward-backward sweep method. Based on the simulation results, it shows that providing optimal control can bring down the spread of Covid-19 by 99.18% with minimal costs 322917.