The catalysed oxidation of CO using mass-selected Pd₁₃ clusters supported on thin MgO films was modelled using a microkinetic simulation of the reaction. The model of the system includes reverse spill-over calculations which were intrinsically incorporated into the formulation of the kinetics. The spill-over model is based on a capture-zone approach including a co-dependence on the variables of the kinetic equations. The experimental values were determined using dual pulsed-molecular beam measurements and recorded at a range of temperatures. The experiment allowed the turn-over frequency and reaction probability to be determined as a function of mole fraction. Comparison of the kinetic model with the experimental data gives excellent agreement and strongly highlights the importance of substrate effects. In particular, the origin of the low temperature catalysis of the Pd clusters is elucidated. The model allows the mole fraction and temperature dependent values such as the sticking coefficients for these clusters to be predicted.