  Fake news spreading, with the aim of manipulating individuals' perceptions of
facts, is now recognized as a major problem in many democratic societies. Yet,
to date, little has been understood about how fake news spreads on social
networks, what the influence of the education level of individuals is, when
fake news is effective in influencing public opinion, and what interventions
might be successful in mitigating their effect. In this paper, starting from
the recently introduced kinetic multi-agent model with competence by the first
two authors, we propose to derive reduced-order models through the notion of
social closure in the mean-field approximation that has its roots in the
classical hydrodynamic closure of kinetic theory. This approach allows to
obtain simplified models in which the competence and learning of the agents
maintain their role in the dynamics and, at the same time, the structure of
such models is more suitable to be interfaced with data-driven applications.
Examples of different Twitter-based test cases are described and discussed.
