We present a general model for the oxidation of CO on low-index platinum single crystal surfaces. In order to take fluctuations into account, it is first formulated in terms of stochastic birth-death processes. A corresponding deterministic limit for large particle numbers can be derived rigorously. The dynamical behavior of the reaction kinetics is investigated by means of a numerical bifurcation analysis of the deterministic limit and stochastic simulations. The computed bifurcation diagrams for Pt(110) and Pt(100) are in qualitative and reasonable quantitative agreement with experimental results. For Pt(110), several types of noise-induced oscillations are obtained.