We conside the kinetics near a first-order poisoning transition for simple surface reaction models which exlude nonreactive desorption. Elucidation of the development and growth of the reactive steady state from a near-poisoned state is achieved via an ‘‘oxidation epidemic’’ analysis of the evolution of an empy patch embedded in the poisoned phase. Associated critical exponents vary strongly with reaction rate, and reflect slow kinetics. The increase in epidemic survival probability with initial patch size is smooth, and described by additional exponents, rather than indicating a critical size for survival.