The two-dimensional monomer-monomer ([ital AB]) surface reaction model without diffusion is considered for infinitesimal, finite, and infinite reaction rates [ital k]. For equal reactant adsorption rates, in all cases, simulations reveal the same form of slow poisoning, associated with clustering of reactants. This behavior is also the same as that found in simulations of the two-dimensional [ital voter] [ital model] studied in interacting-particle systems theory. The voter model can also be obtained from the dimer-dimer or monomer-dimer surface reaction models with infinitesimal reaction rate. We provide a detailed elucidation of the slow poisoning kinetics via an analytic treatment for the [ital k]=0[sup +] [ital AB] reaction and the voter models. This analysis is extended to incorporate the effects of place-exchange diffusion which slows, but does not prevent poisoning. We also show that the [ital k]=0[sup +] [ital AB] reaction with no diffusion is equivalent to the voter model with diffusion at rate 1/2. Identical behavior of the monomer-monomer reaction and the voter model is also found in an epidemic'' analysis, where one considers the evolution of a surface poisoned by one species, except for a small patch. Finally, we apply our findings to elucidate the behavior of the monomer-dimer surfacemore » reaction model for small reaction rates.« less