The modified model for the cosmic-ray production in the Galactic center, presented earlier in detail, is able to describe well the secondary-to-primary ratios and the Galactic gradient data for distances greater than 5 kpc from the Galactic center. In this paper we extend the model to describe electron and positron fluxes. The shape of the extra positron energy spectrum proposed by Tang and Muller is found and discussed. The survival fractions of radioactive nuclei predicted by the model are in agreement with the data. The general consistency of the model for many different experimental features is shown.