We propose a theoretical analysis of the temporal self-focusing phenomena in the iron-doped indium phosphide (InP: Fe) semiconductor for low irradiations with continuous laser beams at infrared wavelengths for optical telecommunication applications such as optical switching and optical routing. Numerical models using two different methods based on charge transport equations are developed. The first method uses the classical finite differences scheme whereas the second method uses a novel algorithm based on Cellular Automata. Owing to the complexity of the non-linear differential system to be solved, full results are not retrieved but promising preliminary results are obtained and reviewed in this paper: they allow us to foresee that self-focusing on the millisecond time scale is possible in InP: Fe.