Recent terrorist attacks carried out on behalf of ISIS on American and European soil by lone wolf attackers or sleeper cells remind us of the importance of understanding the dynamics of radicalization mediated by social media communication channels. In this paper, we shed light on the social media activity of a group of twenty-five thousand users whose association with ISIS online radical propaganda has been manually verified. By using a computational tool known as dynamical activity-connectivity maps, based on network and temporal activity patterns, we investigate the dynamics of social influence within ISIS supporters. We finally quantify the effectiveness of ISIS propaganda by determining the adoption of extremist content in the general population and draw a parallel between radical propaganda and epidemics spreading, highlighting that information broadcasters and influential ISIS supporters generate highly-infectious cascades of information contagion. Our findings will help generate effective countermeasures to combat the group and other forms of online extremism.