Abstract
COVID-19 remains a major threat to the world since its emergence in December 2019, especially the lack of identification of a specific treatment, as scientific researchers continue to seek a better understanding of the epidemiological cycle and dynamics of the virus. Mathematical modeling of the COVID-19 disease can provide better insight into the complex dynamics of the virus and define preventive measures that can be used to contain the spread of the disease. In this research article, we propose a model describes the epidemic dynamics of Covid-19 in a population after vaccine deployment, is an extension of the standard SEAIR model incorporating temporary protection vaccine compartment. An optimal control problem is formulated with the aim of minimizing the number of infected individuals while considering intervention costs and the constraints of the total and maximum daily vaccineadministration. We use the penalty method to approximate this constrained optimization problem and derive an optimality system that characterizes the optimal control. Finally, we carry out numerical simulations using reported data on COVID-19 infections and vaccination in France and in Tunisia, compare these two countries in the face of the pandemic.