Influence of age group in the spreading of fake news: contact matrices in social media

Internet has become very popular all over the world, due to the low cost services and the huge number of opportunities it offers. Nowadays, social media represents the main tool of communication; influence the connection among people and the way they assimilate and share information. However, the accessibility to a large amount of information as well as the ease of sharing it through social platforms is very risky, since it makes easier for people to find or encounter false information on databases. During the years, several mathematical models have been introduced in order to understand the spreading of diseases in a given population. At present, this kind of models have been successfully applied to describe the transmission of information and in particular of fake news, too. In both cases, it is well-known that such a transmission substantially change depending on the contacts among different age groups. This paper aims to analyze the diffusion of fake news by age groups. To this end, we consider a classical SIR (Susceptible-Infected-Recovered) model composed by three coupled ordinary differential equations. In the model, we introduce a suitable so-called contact matrix, which represents the probability of contacts among different age groups in a social media population. Moreover, the numerical approach for the construction of the social contact pattern is described. Numerical tests on real data are reported, showing the behaviour of the transit of fake news by age groups for three different social platforms as Twitter, Facebook and Instagram in the US and worldwide.