In this paper, we present a model for propagation of intense and ultrashort laser pulses ionizing dielectrics. We consider early ion- ization so that this process is sufficiently weak to avoid requiring a complete description of the ionization process (e.g. the use of ki- netic equations which are very expensive from a computational point of view). As the intensity of the field is small, one photon ioniza- tion is neglected. Ionization may only occur through multi-photonic and collisional ionization. The conduction band is discretized and multiple-rate equations are written for electron densities. The wave- field evolves through Maxwell equations.