We present statistical evidence and dynamical models for the management of conflict and a division of labor (task specialization) in a primate society. Two broad intervention strategy classes are observed--a dyadic strategy--pacifying interventions, and a triadic strategy--policing interventions. These strategies, their respective degrees of specialization, and their consequences for conflict dynamics can be captured through empirically-grounded mathematical models inspired by immuno-dynamics. The spread of aggression, analogous to the proliferation of pathogens, is an epidemiological problem. We show analytically and computationally that policing is an efficient strategy as it requires only a small proportion of a population to police to reduce conflict contagion. Policing, but not pacifying, is capable of effectively eliminating conflict. These results suggest that despite implementation differences there might be universal features of conflict management mechanisms for reducing contagion-like dynamics that apply across biological and social levels. Our analyses further suggest that it can be profitable to conceive of conflict management strategies at the behavioral level as mechanisms of social immunity.