A kinetic model based on the Particles on Demand method is introduced for gas phase detonation hydrodynamics in conjunction with the Lee-Tarver reaction model. The proposed model is realized on two-and three-dimensional lattices and is validated with a set of benchmarks. Quantitative validation is performed with the Chapman-Jouguet theory up to a detonation wave speed of Mach 20 in one dimension. Two-dimensional outward expanding circular detonation is tested for isotropy of the model as well as for the asymptotic detonation wave speed. Mach reflection angles are verified in setups consisting of interacting strong bow shocks emanating from detonation. Spherical detonation is computed to show viability of the proposed model for three dimensional simulations.