A mathematical model is developed to describe the reaction dynamics in the vicinity of the triple-phase boundary (TPB), which is an important part of the pore scale structure of the catalyst layer in proton exchange membrane fuel cells. The model incorporates coupled diffusion, migration, and reaction phenomena of the chemical components in an undersaturated air pore and ionomer. One challenging feature of the work is the description of the TPB by a system of nonlinear partial differential equations (PDEs), coupling bulk, and surface-diffusion phenomena, which offers an approach to study the rarely investigated proton surface diffusion along the air pore surface. A numerical technique is implemented, taking into account the particular form of the domain, in order to solve the nonlinear PDE system efficiently. Several numerical results are discussed, including a sensitivity analysis with respect to the physical reference case and geometric parameters. The results indicate that surface diffusion might play a major role for the reaction kinetics, but only if the air pore is void of liquid water. In contrast, the formation of liquid water in the gas pores will turn surface diffusion into bulk diffusion, with the latter resembling the Grotthus mechanism.