The productivity factor is very important at the mathematical simulation of scientific community evolution. In Ref. 1 the productivity index has been incorporated into the model exogenously to formulate the criterion of dynamic optimization of the scientific community age structure. In this paper we are going to include the productivity (as well as the age) in the individual state space and to derive the main dynamic equation which takes into account the stochastic fluctuations of scientific community members' productivity and some modifications of the Fokker-Planck equation. An approximation method for the evolution model is suggested with the aid of which the computational experiment is carried out. The discussion of experimental results and possible ways for improvement and extension of model are presented.