Rumor Spreading in Social Networks with Individual Privacy Policies

Humans are social animals that love to disseminate ideas and news, as proved by the huge success of social networking websites such as Facebook or Twitter. On the other hand, these platforms have emphasized the dark side of information spreading, that is the diffusion of private facts and rumors in the society. Usually users of these social networks can set a level of privacy, and decide to whom to show their private facts, but they cannot control how their friends will use this information: they could spread it through other social websites, medias or simply with face-to-face communication. The classic Susceptible-Infectious-Recovered (SIR) epidemic model can be adopted for modeling the spread of information in a social network: susceptible individuals do not know the information, then are susceptible to be informed; infectious individuals know and spread the information, while recovered individuals already know the information but do not spread it anymore. A susceptible individual in contact with an infectious one can become infectious with a transmission probability, while an infectious individual naturally recovers from infection with a recovery rate, turning into a recovered individual. We extend this compartmental model in order to represent several kinds of privacy policies, from unsafer to more rigorous: each individual belongs to a class that models the privacy behavior by tuning the transmission probability, the recovery rate and the susceptibility to information, that specifies the interest of the individual on the information. We calculate a privacy score for each individual based on the privacy policies of her neighbors, so as to infer the local robustness to the spread of personal information. We test our model by means of stochastic simulations on synthetic contact networks and on a small partition of the Facebook social network, provided by few hundreds of volunteers that replied to an online survey.