We study the networks of Twitter users posting information about Ransomware and Virus and other malware since 2010. We collected more than 200k tweets about 25 attacks measuring the impact of these outbreaks on the social network. We used the mention network as paradigm of network analysis showing that the networks have a similar behavior in terms of topology and tweet/retweet volumes. A detailed analysis on the data allowed us to better understand the role of the major technical web sites in diffusing the news of each new epidemic, while a study of the social media response reveal how this one is strictly correlated with the media hype but it is not directly proportional to the virus/ransomware diffusion. In fact ransomware is perceived as a problem hundred times more relevant than worms or botnets. We investigated the hypothesis of Early Warning signals in Twitter of malware attacks showing that, despite the popularity of the platform and its large user base, the chances of identifying early warning signals are pretty low. Finally we study the most active users, their distribution and their tendency of discussing more attack and how in time the users switch from a topic to another. Investigating the quality of the information on Twitter about malware we saw a great quality and the possibility to use this information as automatic classification of new attacks.