Differences in catalyst deactivation kinetics in solid acid catalysis are studied with catalyst models that allow for lateral interaction between protons. Deactivation of a solid acid catalyst with laterally interacting protons induces inhomogeneity of proton reactivity that develops with time. As a consequence, product selectivity changes and deactivation will accelerate. This is demonstrated by simulations of the deactivation kinetics of the alkylation reaction of propylene with isobutane. The effect of lateral interactions between protons arises because initial catalyst deactivation is not caused by pore blocking or coke deposition but by a molecular mechanism where protons are consumed due to the formation of stable nonreactive carbenium ions. High selectivity to alkylate requires a catalyst with protons of high reactivity. When protons become consumed by formation of stable deactivating carbenium ions, initially reactive protons are converted into protons of lower reactivity. The latter only catalyze deactivating oligomerization reactions. Simulations that compare the deactivation kinetics of a catalyst model with laterally interacting protons and a catalyst model that contains protons of similar but different reactivity, but that do not laterally interact, are compared. These simulations demonstrate that the lateral interaction catalyst model is initially more selective but also has a lower stability. Catalyst deactivation of the alkylation reaction occurs through two reaction channels. One reaction channel is due to oligomerization of reactant propylene. The other deactivation reaction channel is initiated by deprotonation of intermediate carbenium ions that increase alkene concentration. By consecutive reactions, this also leads to deactivation. The hydride transfer reaction competes with oligomerization reactions. It is favored by strongly acid sites that also suppress the deprotonation reaction. Within the laterally interacting proton catalyst model, when reactive protons become deactivated, weakly reactive protons are generated that only catalyze the deactivating alkene oligomerization and consecutive reactions. This rapid formation of the weakly reactive protons is the cause of decreasing selectivity with reaction time and increased rate of deactivation. Solutions of the mean field kinetic equations as well as stochastic simulations are presented. Comparative simulations with a reduced number of neighbors of the protons illustrate decreased deactivation rates when the proton density decreases. Island formation of adsorbed reaction intermediates on the catalyst surface is observed in stochastic kinetics simulations. When alkylation selectivity is high, this island formation increases the rate of catalyst deactivation in comparison to the rate of deactivation according to the mean field studies. A nonlinear dynamics model of proton dynamics is provided, which shows that the differences between stochastic and mean field simulations are due to frustrated proton state percolation.