To systemly investigate the influence of the mesostructure and the shock loadings on the shock initiation and detonation of polymer bonded explosives (PBXs), a modified Duan-Zhang-Kim（DZK）mesoscopic reaction rate model is proposed. A burn-up and a porosity factors are introduced to describe effects of the outer burning on the surfaces of grains of the explosive at the low-pressure slow reactive stage and the initial charge density, respectively. The calculated pressure-time histories inside the HMX-based PBXC03 explosive samples using the modified model with one set of parameters are in good agreement with the experimental data, which indicates that this model can be used to well predicate the influence of the particle size, the porosity and the shock loading on the shock initiation (i.e., ignition and detonation growth) processes of PBXs. Moreover, it is also observed that the detonation grows fastest in the explosive with a moderate porosity. And the smaller the particle size of the explosive is, the more difficult the explosive can be ignited, in which the detonation grows fastest once the explosive is ignited.