A virus dynamics model for information diffusion in online social networks

Abstract

Social media are increasingly influencing people’s preferences and decisions. Modeling information diffusion on social media networks allows to understand the impact of viral information on individuals behaviors in economic, political and social fields. The aim of this paper is to propose a mathematical viral model to characterize the dynamic of information diffusion on social media platforms resulting from the spread of a viral information. To this end, the problem will be modelled by four differential equations that describe the interactions between ”Uninfected Users”, ”Infected Users”, ”Inert Users” and ”free viral information” based on the similarity between a virus dynamics and people interaction on social media networks. A saturated infection rate is incorporated into the model. First, the problem well-posedness is investigated in terms of existence, positivity and boundedness of solution. Moreover, the reproduction number R0 associated to our problem is calculated using the next generation method. Next, the equilibrium points are calculated and their existence is proved. Therefore, the stability analysis and uniform persistence of the model are investigated according to R0 threshold. Finally , some numerical simulations are carried out in order to illustrate the analytical results. It was revealed that our proposed model may be conductive to understand the viral information diffusion behavior on social media networks. The presented mathematical modeling approach is the first investigation of a virus dynamical model that is used to describe the viral information behavior.