We describe a novel graph-based event detection approach which can accurately identify and track dynamic outbreaks (where the affected region changes over time). Our approach enforces soft constraints on temporal consistency, allowing detected regions to grow, shrink, or move while penalizing implausible region dynamics. Using simulated contaminant plumes diffusing through a water distribution system, we demonstrate that our method improves both detection time and spatial-temporal accuracy when tracking dynamic water-borne outbreaks.