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Sick of Facebook? Read on...

If Facebook is a disease, then most of us know the symptoms: obsessive checking, a compulsion to share trivialities, and confusion about what's real and what isn't. But if Facebook is a disease, then why not use epidemiological methods to try and predict its future? This is what two scientists from Princeton University, New Jersey, have done. And they predict that Facebook is heading for a "rapid decline": between 2015 and 2017 it will lose 80% of the users it had when it was at its peak in 2012.

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The idea that Facebook and other social networking sites are like diseases isn't purely metaphorical. An infectious disease spreads through contacts between people, and so does the usage of something like Facebook: people join because other people they know have joined. And just as with a disease, some people recover. They get bored, and eventually they quit.

When epidemiologists try and predict the spread of a disease they often use a beautifully straight-forward model. The general idea is to divide the population into three classes: those who are susceptible (not yet ill but not immune), those who are infected, and those who have recovered and are assumed to be immune from then on. A set of equations the describes how people flow from one class to the other.

That flow is different for every disease of course: it depends on the infection rate typical for the disease (roughly speaking, how many people are infected by a sick person on average) and the recovery rate (how long it takes on average before someone gets better). The values of these parameters can be estimated by looking at real-life data. Once you have the estimates you can simulate the course of the disease, predict if it is likely to escalate or fizzle out, and you can also work out things like how many people should be vaccinated to prevent a disease from spreading. (See this article for more detail.)

Online networking is infectious just as a disease is, but there is an important difference when it comes to recovery. With a normal disease people recover, on average, in some specified time period. With social networking, however, recovery is infectious too. People get bored because their friends do, or at least this is what existing data seem to suggest. The authors of the new study, John Cannarella and Joshua A. Spechler, therefore used a tweaked version of the traditional SIR model (SIR is an acronym for susceptible, infected, recovered), which takes account of this infectious recovery.

In order to use their model the researchers had to estimate the rate of infection and the rate of infectious recovery. You'd think that this requires information from Facebook itself, but the researchers used publicly available search query data from Google instead. It tells you the relative number of Google search queries for a given search terms (such as "Facebook"), and therefore, so the researchers claim, provides a good measure for the web traffic to a site like Facebook. The added advantage, according to the researchers, is that people who are a member of Facebook but never use it are not counted in this data, whereas they would be counted if you only looked at the number of Facebook accounts.

The Google data suggests that Facebook has already been in decline since 2012, so it gives infromation not only about the uptake of Facebook but also about the loss of active users. The researchers chose their parameters so that the model, when applied to a time period in the past, best matched the data suggested by Google. They then extrapolated the model into the future, and this is what led to the prediction of a rapid decline.

Mathematical modelling is a tricky business, of course, because everything depends on the underlying assumptions. As the statistician George Box once said, "all models are wrong, but some are useful." But Cannarella and Spechler did test the strength of their model on a social networking site that has already all but died out: MySpace. And they claim that it simulates MySpace's life cycle well enough to validate the model. But if you try you could probably come up with plenty of arguments why Facebook and Myspace are two different kettle of fish, or other reasons why the model may not be valid.

If you are one of those people who believes that online social networking will ultimately lead to the downfall of civilisation, then there is another bit of good news arising from the predictions. Assuming that recovery is infectious, it stands to reason that one might be able to "vaccinate" the population against recovery, just as one can vaccinate a population against infection. Perhaps Facebook and other networking sites could come up with a devious strategy of social engineering, to prevent their dying out. But this, so the researchers say their model predicts, is impossible. If Facebook is going to go, it's going to go.

You can read Cannarella and Spechler's paper on the arxiv pre-print server. Or you can simply wait until 2017 to see if their predictions have come true. And if you like this article, then why not follow us on Facebook? Or read a reply from Facebook, predicting imminent doom for Princeton University.

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