This paper investigates the detection of communication outbreaks among a small team of actors in time-varying networks. We propose monitoring plans for known and unknown teams based on generalizations of the exponentially weighted moving average (EWMA) statistic. For unknown teams, we propose an efficient neighborhood-based search to estimate a collection of candidate teams. This procedure dramatically reduces the computational complexity of an exhaustive search. Our procedure consists of two steps: communication counts between actors are first smoothed using a multivariate EWMA strategy. Densely connected teams are identified as candidates using a neighborhood search approach. These candidate teams are then monitored using a surveillance plan derived from a generalized EWMA statistic. Monitoring plans are established for collaborative teams, teams with a dominant leader, as well as for global outbreaks. We consider weighted heterogeneous dynamic networks, where the expected communication count between each pair of actors is potentially different across pairs and time, as well as homogeneous networks, where the expected communication count is constant across time and actors. Our monitoring plans are evaluated on a test bed of simulated networks as well as on the U.S. Senate co-voting network, which models the Senate voting patterns from 1857 to 2015. Our analysis suggests that our surveillance strategies can efficiently detect relevant and significant changes in dynamic networks.