Optimal control problem for COVID-19 with multiple time-delays in state and control

The primary motivation of this paper is to identify the most effective implementation of delayed preventive measures, including active screening and testing, mask-wearing, and vaccination for COVID-19, in a way that minimizes the number of infected and exposed individuals, and maximizes the count of recovered individuals. Our goal is to comprehend the impact of delays on the epidemic’s spread and to offer guidance to health authorities on what steps to take if they implement COVID-19 preventive measures too late. We achieve this by employing optimal control theory on a SEIR model that illustrates the dynamics between susceptible, infected, exposed, and recovered individuals within the population. We set up our optimal control problem with multiple time delays in both the state and control variables, then, we used Pontryagin’s Maximum Principle to determine the solution to the delayed optimal control problem with multiple state-control constraints. Our results of simulation show that to control epidemic propagation when preventive measures are delayed, we should take immediate action after delay phase by enforcing mask wear and starting vaccinations to cover a significant portion of the population as quickly as possible. We should then implement active screening and testing measures to further control the spread.