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Modelling human mobility is crucial in several areas, from urban planning to epidemic modelling, traffic forecasting, and what-if analysis. Existing generative models focus mainly on reproducing the spatial and temporal dimensions of human mobility, while the social aspect, though it influences human movements significantly, is often neglected. Those models that capture some social perspectives of human mobility utilize trivial and unrealistic spatial and temporal mechanisms. In this paper, we propose the Spatial, Temporal and Social Exploration and Preferential Return model (STS-EPR), which embeds mechanisms to capture the spatial, temporal, and social aspects together. We compare the trajectories produced by STS-EPR with respect to real-world trajectories and synthetic trajectories generated by two state-of-the-art generative models on a set of standard mobility measures. Our experiments conducted on an open dataset show that STS-EPR, overall, outperforms existing spatial-temporal or social models demonstrating the importance of modelling adequately the sociality to capture precisely all the other dimensions of human mobility. We further investigate the impact of the tile shape of the spatial tessellation on the performance of our model. STS-EPR, which is open-source and tested on open data, represents a step towards the design of a mechanistic data-driven model that captures all the aspects of human mobility comprehensively.