Proximity-based contact tracing relies on mobile-device interaction to estimate the spread of disease. ShareTrace is one such approach that improves the efficacy of tracking disease spread by considering direct and indirect forms of contact. In this work, we utilize the actor model to provide an efficient and scalable formulation of ShareTrace with asynchronous, concurrent message passing on a temporal contact network. We also introduce message reachability, an extension of temporal reachability that accounts for network topology and message-passing semantics. Our evaluation on both synthetic and real-world contact networks indicates that correct parameter values optimize for algorithmic accuracy and efficiency. In addition, we demonstrate that message reachability can accurately estimate the risk a user poses to their contacts.