  We provide a quantitative theoretical model study of the dynamical magnetic
properties of optimally annealed Ga$_{1-x}$Mn$_x$As. This model has already
been shown to reproduce accurately the Curie temperatures for
Ga$_{1-x}$Mn$_x$As. Here we show that the calculated spin stiffness are in
excellent agreement with those which were obtained from ab-initio based
studies. In addition, an overall good agreement is also found with available
experimental data. We have also evaluated the magnon density of states and the
typical density of states from which the "mobility edge", separating the
extended from localized magnon states, was determined. The power of the model
lies in its ability to be generalized for a broad class of diluted magnetic
semiconductor materials, thus it bridges the gap between first principle
calculations and model based studies.
