Instruments and Systems: Monitoring, Control, and Diagnostics Annotation << Back Mathematical Modeling of the COVID-19 Aerosol Cloud Movement in the Closed Space S.V. VERETEKHINA, V.I. ZAJKOVSKIJ, S.M. KUR’YAN, A.D. KOZLOV The author considers the mathematical modeling of the COVID-19 aerosol cloud movement in a closed space, formalizes the initial and boundary conditions for software solutions. Modeling methods are described taking into account the laws of physics of motion of air molecules: the change in the mass of a substance in the air for a short period of time and the change in the profi t/loss of a substance in the thrown volume. Methods used: the first method is based on the description of the nature of changes in time of concentrations averaged over the entire volume, and the second method is based on the description of the field of instantaneous and integral concentrations, based on the convective-diffusion processes of their formation. The following parameters are described for further research. A new vector is being developed for studying the movement of the COVID-19 aerosol cloud in a confined space. The study presents a simulation of the movement of infected air COVID-19 in 4 frames over a short period of time: the initial time is 0, after 0.5 s, after 1 s, after 1.5 s. The study provides a simulation frame and a listing of the program. Novelty: elements of the novelty of the presented solution for predicting the movement of an aerosol cloud of infection are taking into account the following factors: gravitational settling of cloud particles, interaction of the infected cloud with the walls of the room, air exchange in the external environment taking into account natural and/or forced ventilation, taking into account instantaneous concentrations and diffusion processes. The dependences of the molecular and turbulent diffusions in a closed space are derived. The conditions of dependences on the temperature in homogeneity of the air, the total area of the room, and the mode of movement of air masses are formed. The calculations are based on the equations of mathematical physics-green’s functions. The simulation was performed by dividing the volume and time into a grid, after which a difference equation was compiled, which is solved by the Gauss method. The Laplace equation was modeled. Result: during the initial simulation, the study provides simulation frames and a program listing. The formalization of initial and boundary conditions allows us to develop analytical and numerical methods for describing the fields of instantaneous concentration and exposure doses. The proposed software (program listing) is applicable for computers, complexes, and systems. In conclusion, the direction vector of the next study is formed. Practical signifi cance: further mathematical modeling is planned to be carried out using the dynamic programming method, the program listing will be refined to the specifi ed parameters, which allows optimizing labor and financial costs for research. Keywords: mathematical predictive modeling, COVID-19, formalization of initial and boundary conditions. DOI: 10.25791/pribor.8.2021.1286 Pp. 44-49.