Competing for Attention in Social Media under Information Overload   Conditions
  Although the many forms of modern social media have become major channels for the dissemination of information, they are becoming overloaded because of the rapidly-expanding number of information feeds. We analyze the expanding user-generated content in Sina Weibo, the largest micro-blog site in China, and find evidence that popular messages often follow a mechanism that differs from that found in the spread of disease, in contrast to common believe. In this mechanism, an individual with more friends needs more repeated exposures to spread further the information. Moreover, our data suggest that in contrast to epidemics, for certain messages the chance of an individual to share the message is proportional to the fraction of its neighbours who shared it with him/her. Thus the greater the number of friends an individual has the greater the number of repeated contacts needed to spread the message, which is a result of competition for attention. We model this process using a fractional susceptible infected recovered (FSIR) model, where the infection probability of a node is proportional to its fraction of infected neighbors. Our findings have dramatic implications for information contagion. For example, using the FSIR model we find that real-world social networks have a finite epidemic threshold. This is in contrast to the zero threshold that conventional wisdom derives from disease epidemic models. This means that when individuals are overloaded with excess information feeds, the information either reaches out the population if it is above the critical epidemic threshold, or it would never be well received, leading to only a handful of information contents that can be widely spread throughout the population. 
Ling Feng, Yanqing Hu, Baowen Li, H. Eugene Stanley, Shlomo Havlin and   Lidia A. Braunstein
physics.soc-ph cs.SI