Optimal control strategy for the administration of the third vaccine dose in the treatment of pandemic COVID-19

In this paper, we propose a mathematical model of COVID-19 infection, taking into account the division of the population according to vaccination criteria. Our goal is to demonstrate the positive effect of receiving the third dose of the Corona vaccine. We proposed two strategies to limit the spread of the COVID-19 pandemic respectively awareness programs on the importance of the third dose of the vaccine and the delivery of treatment to infected individuals who have health problems. Pontryagin's maximum principle is applied in order to characterize the optimal controls, and the optimality system is resolved using an iterative approach. At last, numerical simulations are executed to verify the theoretical analysis using MATLAB.