In this paper, two nonstandard finite difference schemes for approximating the solution of a mathematical model of HIV infection are presented. The technique of nonlocal approximation and renormalization of the denominator of the discrete derivative was employed. The new schemes were found to possess the elementary stability property and also to preserve the positivity property, which are essential requirements for solving epidemic disease models. Unlike 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.
