In this paper, we treat the following problem: Given a stable Gani-type person- flow model and assuming no negative recruitment, what recruitment distribution at the $n$-step is capable of generating a staff-mix that closely follows the desired structure? We relate this problem to the challenge of universities in Nigeria towards attaining the desired academic staff-mix by rank specified by the National Universities Commission (NUC). We formulate a population-dynamic model consisting of aggregate-fractional flow balance equations within a discrete-time Markov chain framework for the system. We use MATLAB as a convenient platform to solve the system of equations. The utility of the model is illustrated by means of academic staff flows in a university-faculty setting in Nigeria.