The article examines a mathematical compartment model of the spread of the COVID-19 coronavirus. The article consists of six paragraphs. In this study, epidemic outbreaks are studied from an interdisciplinary point of view using an extension of the susceptible-infected-recovered-deceased (SEIRD) model, which is a mathematical chamber model based on the average behavior of the studied population group. Many infectious diseases are characterized by an incubation period between exposure and the appearance of clinical symptoms. Subjects exposed to infection are much more dangerous to the public compared to subjects who have clinical symptoms. A nonlinear system of SEIRD differential equations is considered. For the numerical solution of a direct problem, the fourth-order Runge-Kutta method is considered. In modeling, the relationship is derived based on the laws of the subject area and allows you to determine the nature of changes in the framework of the work, depending on its parameters. The inverse problem is posed to determine the coefficients of this system. The inverse problem was solved by the method of a genetic algorithm. The method of the genetic algorithm is described. Numerical results are obtained and a comparative analysis with accurate data is made.