In this work, we present an approach to modelling III-V lasers on silicon based on a travelling-wave rate equation model with sub-micrometer resolution. By allowing spatially resolved inclusion of individual dislocations along the laser cavity, our simulation results offer new insights into the physical mechanisms behind the characteristics of 980 nm In(Ga)As/GaAs quantum well (QW) and 1.3 m quantum dot (QD) lasers grown on silicon. By studying the reduction of the local gain in carrierdepleted regions around dislocation locations and the resulting impact on threshold current increase and slope efficiency at high dislocation densities, we identify two effects with particular importance for practical applications. First, a large minority carrier diffusion length is a key parameter inhibiting laser operation by enabling carrier migration into dislocations over larger areas, and secondly, increased gain in dislocation-free regions compensating for gain dips around dislocations may contribute to gain compression effects observed in directly modulated silicon-based QD lasers. We believe that this work is an important contribution in creating a better understanding of the processes limiting the capabilities of III-V lasers on silicon in order to explore suitable materials and designs for monolithic light sources for silicon photonics.