Killer cure. An epidemiological model predicts Facebook usage will decline precipitously as people "recover" from interest in it.

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Killer cure. An epidemiological model predicts Facebook usage will decline precipitously as people "recover" from interest in it.

Facebook Spreads—and May Die Out—Like a Disease

Staff Writer

The thought has probably run through your head on some fruitless afternoon when you find yourself clicking on Facebook for the ninth time in 15 minutes: Facebook is a disease. That characterization might be particularly apt, according to two graduate students at Princeton University. Using a simple epidemiological model, they argue that use of the hegemonic social networking site has spread like a contagion. Moreover, their model suggests that, just like the Myspace site before it, Facebook will suffer a colossal fall within the next few years. Other researchers caution that's not a sure bet.

It's no surprise that an epidemiological model can be applied to a social phenomenon like use of a website. After all, infectious diseases often spread through person-to-person contact, making them social phenomena. At the same time, for an individual, interest in an idea or service can come and go like a disease, dissipating after he or she grows bored.

A very simple mathematical model of epidemics appears to account for the evolution of Myspace and Facebook, argue John Cannarella and Joshua Spechler, graduate students in mechanical and aerospace engineering at Princeton University in a paper posted to the arXiv preprint server. In the model, they assume that there are three types of people: "susceptible" people, S, who have not yet started using a social networking site; "infected" people, I, who are using it; and "recovered" people, R, who have either stopped using the site or refused to do so in the first place. The sizes of the groups change as the "disease" spreads. For example, because each new infection depends on a susceptible person encountering an infected person, at any moment the number of susceptible people decreases at a rate proportional to the number of infected people times the number of susceptible people. The number of infected people gets a boost by that same rate, but simultaneously suffers a loss as people recover.

The researchers' model would be identical to the so-called SIR model, which is perhaps the simplest in epidemiology, except that they add a twist. In the SIR model, people recover on their own, as if recovering from a cold, so that at any moment the number of recovered people increases at a rate proportional to the number of infected people alone. In their model, Cannarella and Spechler assume that to recover, an infected person has to encounter a recovered person—in terms of a social networking site, you won't stop using it until one of your friends does, an assumption that emphasizes the social nature of the network. In that case, the number of recovered increases at a rate proportional to the number of infected people times the number of recovered people.

The researchers then applied their model to real data. To estimate Myspace and Facebook participation, Cannarella and Spechler relied on the frequency of searches for either name with the Google search engine. Those data were much easier to obtain than actual user numbers, which are proprietary information. They also should more accurately track actual usage of each site and not just the number of members, which could remain high even after people have lost interest. The model neatly fits the rise and fall in usage of Myspace, which peaked in 2008 with 75.9 million unique monthly visits in the United States and decayed to next to nothing by 2011. Similarly, the duo found their model could replicate Facebook's trajectory, which according to the Google search data appears to have plateaued in recent years and has fallen slightly since 2012.

Most striking, the researchers' model predicts that Facebook's use will soon fall much farther and much faster as "recovered" users induce others to give up their Facebook habit. According to the model, Facebook will have lost 80% of its users by sometime between 2015 and 2017.

Time to sell your Facebook stock? Not necessarily, says Marisa Eisenberg, a mathematical epidemiologist at the University of Michigan, Ann Arbor. The researchers' particular take on the SIR model is so simple that it has only one potential outcome: Fast or slow, the epidemic (or social networking site) eventually dies out. It might be more revealing, Eisenberg says, to compare this model to a version in which it is possible for the epidemic or site to persist or grow indefinitely, for example because recovered people can become susceptible again. Still, Eisenberg applauds the effort. "I wouldn't put a lot of stock in saying what's going to happen with Facebook one way or the other," she says, "but the idea of using a SIR framework to study social network usage is cool."

Posted in Math, Social Sciences