Is this the end for Facebook? A mathematical analysis

Since the early 2000s, one of the most popular uses of the Internet has been for online social networking. Since 2009, the most popular online social network has been Facebook; roughly 80% of Internet users worldwide have a Facebook account as of the end of 2014. However, in early 2014, Princeton University graduate students Cannarella and Spechler released a manuscript which claimed that Facebook would decline in popularity to essential “death” by the end of 2017. This claim was based on results obtained from an adaptation of the classic SIR epidemic model. In this paper, we will explore a modified version of this model to take into account a changing population size and the possibility of people leaving the social network, but later returning, and compare this model and its results to those of the original model to either confirm or deny the result that Facebook will fade to obscurity by the end of 2017.