Modelling human mobility is crucial in several scientific areas, from urban planning to epidemic modeling, traffic forecasting, and what-if analysis. On the one hand, existing models focus on the spatial and temporal dimensions of mobility only, while the social dimension is often neglected. On other hand, models that embed a social mechanism have trivial or unrealistic spatial and temporal mechanisms. We propose STS-EPR, a mechanistic model that captures the spatial, temporal, and social dimensions of human mobility together. Our results show that STS-EPR generates realistic trajectories, making it better than models that lack either in the social, the spatial, or the temporal mechanisms. STS-EPR is a step towards the design of mechanistic models that can capture all the aspects of human mobility in a comprehensive way.