Social networks have gradually turned into prime means for the spreading of computer viruses, especially of those that employ social engineering deception strategies. Yet the study of their propagation typically neglects the temporal nature of social interactions, as well as that the susceptibility of online users is not homogenous. Conversely, the study of individual users’ susceptibility to cyber threats typically neglects their connections. Here, we address these limitations with a theoretical framework that captures both heterogenous susceptibility to deception and the time-varying nature of social networks. We model users’ interactions using a time-varying network model and consider two types of viruses. The first mimics threats that can propagate only via connections activated during the infection period. The second instead, considers viruses able to access also information about past connections. We investigate the impact of different categories of susceptibility considering that they might also influence the link formation process. In all cases, we analytically derive the conditions regulating the spreading of the viruses. Interestingly, these are defined by a complex interplay between the features of the cyber threat, the categories of susceptibility and their time-varying connectivity. Furthermore, in some scenarios the coupling between categories creates a complex phenomenology that increases the fragility of the system. Our results have the potential to initiate future efforts aimed at describing more realistically the spreading of computer viruses on online social networks.
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