Modeling the dynamics of user adoption and abandonment in online social networks

We introduce a new compartmental model aimed at examining the dynamics of user adoption and abandonment within online social networks. Our model encompasses two abandonment dynamics: infectious abandonment caused by internal influences from individuals who have already left the network and noninfectious abandonment triggered by mass media, advertisements, or the introduction of new products. We verify the model's validity and explore the existence and stability of its equilibria. To confirm our theoretical framework, we conduct extensive numerical simulations. We demonstrate the model's effectiveness by fitting it to historical data on Facebook's daily active users. Finally, we utilize the derived model parameters to forecast the future numbers of active users on Facebook.