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To conduct a comprehensive study of the significant factors affecting the transfer and diffusion process of aerosol particles in the atmosphere, a mathematical model, numerical and software tools are developed in the paper. Taking into account the physicomechanical properties of harmful substances discarded from industrial production facilities and the characteristics of soil surface, air velocity, and the substance extinction coefficients. When predicting the concentration of harmful substances in the atmosphere, a key factor that affects the transfer and diffusion of aerosol particles in the atmosphere is the velocity of substance transfer in three directions x, y, z, respectively. The problem posed in the paper is solved by the finite-difference method and the results of numerical calculations on a computer are presented in the form of graphs. It was established that the transfer and diffusion processes of aerosol particles in the atmosphere that play an important role are the rate of air mass formation in the surface layer of the atmosphere; the density and linear size of the aerosol particles emitted into the atmosphere; the terrain, which generates the velocity of air propagation in the atmosphere. It was established by computational experiments that the lower the density and mass of a harmful substance particle, the higher its horizontal velocity and the lower its vertical velocity.

Mathematical model for predicting, monitoring and assessing the ecological state of the atmosphere and underlying surface with passive and active impurities is developed in this article; it takes into account the varying rate of particle displacements in the atmosphere. To determine the rate of displacements of fine-dispersed particles in the atmosphere, a system of nonlinear equations has been obtained, which took into account such important factors as: the basic physical-mechanical properties of the particles and the rate of air mass in the atmosphere.