In this work, we study the oscillatory behavior of CO oxidation in a catalyst constituted by Pd crystallites supported within a zeolite matrix by numerical simulation. For that, we perform a numerical bifurcation analysis of the STM (Sales-Turner-Maple) model (Sales, B. C.; Turner, J. E.; Maple, M. B. Surf. Sci. 1982, 114, 381), which was modified by Basset and Imbihl (Bassett, M. R; Imbihl R. J. Chem. Phys. 1990, 93, 811) and Slinko et al. (Slinko, M.; Kurkina, E.; Liauw, M.; Jaeger, N. J. Chem, Phys. 1999, 111, 8105) to, take into account subsurface oxygen, and we extend it to study the effect of diffusion; the final model is a mixed system with ordinary and partial differential equations. We study the influence of diffusion of one species along different directions and the effect of poisoning reaction sites. The bifurcation analysis identifies the fixed points and the kind of Hopf-Andronov bifurcation between oscillatory and steady state behavior. Our results show that as D is increased the amplitude and the period of oscillations are larger with respect to the homogeneous case and that there is a critical fraction of inert sites where the oscillations die and the transition from oscillatory to steady state corresponds to a Hopf bifurcation.