Sustainability & social segmentation in social media contagion: A mathematical and computational study on dual effects of individual needs & peer influence.

Addiction to internet-based social media has increasingly emerged as a critical social problem, especially among young adults and teenagers. Based on multiple research studies, excessive usage of social media may have detrimental psychological and physical impacts. In this study, we are going to explore mathematically the dynamics of social media addiction behavior and explore the determinants of compulsive use of social media from the dual perspectives of individual needs or cravings and peer-related factors or peer pressure. The theoretical analysis of the model without the peer pressure effect reveals that the associated addiction-free equilibrium is globally stable whenever a certain threshold, known as the addictive-generation number, is less than unity and unstable when the threshold is greater than unity. We observed how introduction of peer influence adds a sustainability to the dynamics, and causes a multistability, through which addiction-contagion can proliferate, even below the designated critical threshold. Using simulations over model networks, we demonstrate our finding, even in the presence of social heterogeneity. Finally, we use the reaction-diffusion approach to investigate spatio-temporal dynamics in a synthetic society, in the form of a 2D lattice. Instead of a fast convergence to the steady states, we observe a long transient of social clustering and segmentation, represented by spatio-temporal pattern formation. Our model illustrates how the peer influence factor plays a crucial role and concludes that it is required to consider the peer factors while formulating specific strategies that could be more effective against this addiction and its potential adverse outcomes.