Traditional contact tracing relies on knowledge of the interpersonal network of physical interactions, where contagious outbreaks propagate. However, due to privacy constraints and noisy data assimilation, this network is generally difficult to reconstruct accurately. Communication traces obtained by mobile phones are known to be good proxies for the physical interaction network, and they may provide a valuable tool for contact tracing. Motivated by this assumption, we propose a model for contact tracing, where an infection is spreading in the physical interpersonal network, which can never be fully recovered; and contact tracing is occurring in a communication network which acts as a proxy for the first. We apply this dual model to a dataset covering 72 students over a 9 month period, for which both the physical interactions as well as the mobile communication traces are known. Our results suggest that a wide range of contact tracing strategies may significantly reduce the final size of the epidemic, by mainly affecting its peak of incidence. However, we find that for low overlap between the face-to-face and communication interaction network, contact tracing is only efficient at the beginning of the outbreak, due to rapidly increasing costs as the epidemic evolves. Overall, contact tracing via mobile phone communication traces may be a viable option to arrest contagious outbreaks.