Recently, networks of user interactions in online systems gained a lot of interest from our research community. Such networks are characterized by complex bursty patterns of human user behavior. A lot of models for such networks are based on the activity-driven time-varying network framework, which was introduced in an effort to model human interaction networks more accurately. Mostly, these models rely on intrinsic activity patterns of individuals and disregard external influences. However, such external influences are important factors in more complex interaction scenarios. In this paper, we propose an activity-driven network model by introducing a peer influence mechanism into the network dynamics. In particular, we allow for active individuals to motivate their peers to become active as well. We examine the ramifications of this mechanism on the topological and activity-related properties of synthetically generated networks and reveal its complex influence on the underlying dynamics. As expected, our results show that peer influence has positive effects on formation of network communities. At the same time the changes in activity patterns suggest a complex response of the system to the peer influence mechanism. This interesting preliminary result opens interesting avenues for further research in the future. Our main contributions are (i) the specification of peer influence for an activity-driven network generator, and (ii) the analysis and discussion of the added peer influence mechanism on synthetic networks.