A mathematical model has been developed for training a neural network to predict the concentration of atmospheric pollutants from traffic jams that occur near socially significant objects. An explicit finite-difference scheme is proposed for the numerical solution of a partial differential equation approximating the change in concentration at control points. The stability of the proposed scheme is being studied. A software product for calculating the change in time of the concentration of nitric oxide at given points in the controlled area by the method of fractional steps has been developed. A computational experiment showed the possibility of using the developed software for training a recurrent neural network.