Abstract
The task of managing epidemic security during COVID-19 is considered. The spread of the SARS-CoV-2 virus without and with vaccination is described by mathematical and computer models built on the basis of the epidemic control protocol adopted by the Georgian authorities. The mathematical model of the spread of the SARS-CoV-2 virus is described using the Cauchy problem for a system of ordinary differential equations. For the management of epidemiological safety, a objective function has been built, which takes into account: the financial consequences of introducing a lockdown in the country and the cost of treating the infected. Among the parameters of the model, the governing ones are highlighted. The control parameters are used to minimize the objective function. In the work, mainly theoretical research is given. However, computer simulation and a computational experiment on the proposed computer model with constant parameters allows us to answer the question: what is the number of infected citizens in the country, in which the economy does not need a lockdown, and the recovery prognosis of those infected with the SARS-CoV-2 virus is favorable.