Recently a kinetic model was proposed for describing the hydrogen-oxygen reaction on Pt(111). This model is based on the reactive-site mechanism, i.e. only a very limited number of Pt sites are considered to be catalytically active for the actual water formation reaction. Here we consider the implications of the model for the H-2-O-2 reaction at low temperatures (<300 K) in more detail. Additional autocatalytic reaction steps between oxygen, H2O and reaction intermediates are taken into account which enable the complete conversion of oxygen to H2O. The model is consistent with the observed transition from a reaction mechanism through which H2O can be formed at temperatures as low as 130 K to the much slower diffusion-controlled mechanism which was found to dominate at low oxygen coverages at higher temperatures (>250-300 K). Using the same reaction parameters, data sets of Ogle et al. and Germer et al. can be simulated quite well with the model. The actual water-formation reaction (at the reactive site), the reaction between H2O and O atoms (at the ''reaction front'') and the adsorption of hydrogen appear to be the rate-limiting steps. The simulations indicate that the adsorption of hydrogen proceeds via a rather complex process, which is difficult to incorporate correctly in the model.