The effect of inert sites (random impurities) in the global oscillations in the oxidation of CO on Pt(100) is studied analytically via a stability analysis of the underlying mean field model. The analysis shows that the introduction of a fraction theta (d) of inert sites can reduce considerably the extent of the oscillatory region on the bifurcation diagram. The study of a mean field model explains some of the basic features that arise upon increasing the density of impurities on the catalytic surface, and it allows the analytical calculation of the bifurcation diagram. The analytical solution of the model reproduces well cellular automata simulations. In particular, we show the existence of a critical concentration of inert sites at which the oscillatory region vanishes and oscillations are no longer possible, due to the inability of the lattice to reach the minimum local concentration of CO required to trigger the surface reconstruction mechanism. We have evaluated this maximum defect concentration in the mean field approximation to be exactly theta (d)*=1-theta (+)(CO), where theta (+)(CO) is the minimum CO concentration required to trigger the (hex) to (1x1) Pt substrate transition. For the set of parameters chosen, we find here theta (d)*=0.6, which is in perfect agreement with our earlier simulation findings.