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Aggression in online social networks has been studied mostly from the perspective of machine learning which detects such behavior in a static context. However, the way aggression diffuses in the network has received little attention as it embeds modeling challenges. In fact, modeling how aggression propagates from one user to another, is an important research topic since it can enable effective aggression monitoring, especially in media platforms which up to now apply simplistic user blocking techniques. In this paper, we address aggression propagation modeling and minimization on Twitter, since it is a popular microblogging platform at which aggression had several onsets. We propose various methods building on two well-known diffusion models, Independent Cascade (IC) and Linear Threshold (LT), to study the aggression evolution in the social network. We experimentally investigate how well each method can model aggression propagation using real Twitter data, while varying parameters, such as seed users selection, graph edge weighting, users' activation timing, etc. It is found that the best performing strategies are the ones to select seed users with a degree-based approach, weigh user edges based on their social circles' overlaps, and activate users according to their aggression levels. We further employ the best performing models to predict which ordinary real users could become aggressive (and vice versa) in the future, and achieve up to AUC=0.89 in this prediction task. Finally, we investigate aggression minimization by launching competitive cascades to "inform" and "heal" aggressors. We show that IC and LT models can be used in aggression minimization, providing less intrusive alternatives to the blocking techniques currently employed by popular online social network platforms.