LOCAL STABILITY AND OPTIMAL CONTROL STRATEGY FOR A SARS-CoV-2 EPIDEMIC

This article assesses the effect of vaccination on the control of an infectious disease using a new mathematical model in which immunity is not acquired permanently. In this model, the number of elementary reproductions \mathcal{R}_0 is a major indicator of the extinction or propagation of the infection in a population. In this document, the cost of control is also defined in order to propose an optimal value. Variable states are also simulated as a function of the evolution of the disease in relation to the strength of the infection.