The spread of fake news and the interplay with personal competence: Boltzmann-type kinetic models and Monte Carlo simulations

Nowadays, Internet is becoming the primary source of information, and the use of social networks makes possible to come every day in contact with a great deal of news, much of which turns out to be fake. In recent years, for this reason, more and more fake news has been studied, trying to understand how to recognize them, how they propagate and how they affect people, especially their knowledge. In the first part of this thesis, it is analyzed through kinetic theory how individual's competence varies in the interaction with a fake news, characterized by a degree of falsehood. This analysis shows that, over long periods of time, there is a polarization in agents' knowledge toward the highest degree of competence (those who are perfectly able to discern between true and false news) and toward the lowest degree of competence (those who are unable in any way to recognize the reliability of a news). This analytically obtained behavior is also verified numerically through Monte Carlo simulations. The second part is devoted to the study of the popularity of fake news on a social-network. At first, we make the assumption that, who is not sufficiently competent, will share the news. From the study of the evolution of the popularity conditional on a given degree of falsity of the news, the results show that, a totally false news, tends in a long time to completely lose popularity, since no one will share it, while, if the news is true, the average popularity conditional on that degree of falsity will not cancel out. In conclusion, we propose 3 alternative models for the popularity of the fake news.