An induction parameter model has been constructed for the simulation of shock-induced combustion that incorporates the repro-modeling approach for the description of the energy release phase. The model applies only explicit, algebraic functions for the description of the chemical kinetics. These functions parameterize a set of data calculated from homogeneous combustion simulations using a complete and detailed reaction mechanism. Based on this method a model has been created for the simulation of shock-induced combustion of hydrogen in an argon atmosphere. The parameterized model approximates the results of the full chemistry very closely, but the algebraic functions can be computed in a fraction of the time of the full chemistry solution. We use the parameterized model in one- and two-dimensional reactive flow simulations. The results simulate experimental results well, including transitions to detonations and the propagation of detonation waves.