We formulate and analyze an unconditionally stable nonstandard finite difference method for a mathematical model of HIV
transmission dynamics. The dynamics of this model are studied using the qualitative theory of dynamical systems. These
qualitative features of the continuous model are preserved by the numerical method that we propose in this paper. This
method also preserves the positivity of the solution, which is one of the essential requirements when modeling epidemic
diseases. Robust numerical results confirming theoretical investigations are provided. Comparisons are also made with the
other conventional approaches that are routinely used for such problems.