In this paper, we construct a nonstandard finite difference (NSFD) scheme for approximating the solution of a mathematical model of HIV infec- tion. 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. The new schemes where found to possess the elementary stability property and also preserve the positivity property, which are essential requirements for epidemic disease models. Unlike the other conventional approaches that are routinely used for solving such problems, the solutions provided by the new schemes have the property of positivity for any step size.
