Is Facebook coming to an end? Recently, this paper has received a lot of attention (e.g. from WSJ). Basically, the authors conclude that Facebook will lose 80% of its members by 2017. 
They base their claims on an extrapolation of the SIR model, a compartmental model frequently used in epidemiology. Their data is drawn from Google searches for "Facebook", and the authors use the demise of Myspace to validate their conclusion.
Question:
Are the authors making a "correlation does not imply causation" mistake? This model and logic may have worked for Myspace, but is it valid for any social network?
Update: Facebook hits back

In keeping with the scientific principle "correlation equals causation," our research unequivocally demonstrated that Princeton may be in danger of disappearing entirely.
We don’t really think Princeton or the world’s air supply is going anywhere soon. We love Princeton (and air),” and adding a final reminder that “not all research is created equal – and some methods of analysis lead to pretty crazy conclusions.

 A: The question isn't "if" but "when".
That it will end is already guaranteed.
http://www.ted.com/talks/geoffrey_west_the_surprising_math_of_cities_and_corporations.html
I take umbrage with the use of the SIR model.  It comes with assumptions.
One of the assumptions is that eventually everyone is "recovered".  Infections are not perpetual, while technology adoption can be (consider the automobile for example).
If the business is doomed to eventually die, then when going through death throes the relationships between susceptible, infected, and recovered might be adequately modeled by a particular SIR model.  This does not mean the model is descriptive of any of the seasons before end-of-life.  It does not take into account other forces - the context.  Facebook was part of the context of end of "Myspace" and so while an SIR was appropriate for Myspace-only use, it was not for Social-Network use because many users had accounts on both, and switched to FB-dominant usage.
I dug through the zombie-model, and even through some non-zombie SIR fits, and a time and population punctuated-windowed SIR is more appropriate there.  It is not a universal model, and it has strengths and weaknesses.  That means that the SIR is imperfect even for the systems that it was engineered to model.  Such fundamental imperfection for its target suggests that without careful use, application outside the target area can be, ceteris paribus, more problematic than other model.
A: Well, this paper establishes the fact that the number of Google searches on Facebook fits a certain curve nicely. So at best it can predict that the searches on Facebook will decline by 80%. Which might be feasible, because Facebook might become so ubiquitous that nobody would need to search about it. 
The problem with such type of models is that they assume that no other factors can influence the dynamics of the observed variable. This assumption is hard to justify when dealing with data related to people. For example, this model assumes that Facebook cannot do anything to counter the loss of its users, which is a very questionable assumption to make.
A: To answer your question

This model and logic may have worked for MySpace, but is it valid for
  any social network?

Probably not. Historical data can only predict future events if the 'environment' is similar.  This paper assumes that the total of Google users and queries is a constant, which of course it is not.  Now this article may say more about Google than about Facebook.
However, based on the rapid rise and fall of many other social networks like MySpace and others I think one can safely assume that there is a big chance Facebook will no longer be the dominant social network in 5 years.
A: The answers so far have focused on the data itself, which makes sense with the site this is on, and the flaws about it.
But I'm a computational/mathematical epidemiologist by inclination, so I'm also going to talk about the model itself for a little bit, because it's also relevant to the discussion.
In my mind, the biggest problem with the paper is not the Google data. Mathematical models in epidemiology handle messy data all the time, and to my mind the problems with it could be addressed with a fairly straightforward sensitivity analysis.
The biggest problem, to me, is that the researchers have "doomed themselves to success" — something that should always be avoided in research. They do this in the model they decided to fit to the data: a standard SIR model.
Briefly, a SIR model (which stands for susceptible (S) infectious (I) recovered (R)) is a series of differential equations that track the health states of a population as it experiences an infectious disease. Infected individuals interact with susceptible individuals and infect them, and then in time move on to the recovered category.
This produces a curve that looks like this:

Beautiful, is it not? And yes, this one is for a zombie epidemic. Long story.
In this case, the red line is what's being modeled as "Facebook users". The problem is this:
In the basic SIR model, the I class will eventually, and inevitably, asymptotically approach zero.
It must happen. It doesn't matter if you're modeling zombies, measles, Facebook, or Stack Exchange, etc. If you model it with a SIR model, the inevitable conclusion is that the population in the infectious (I) class drops to approximately zero.
There are extremely straightforward extensions to the SIR model that make this not true — either you can have people in the recovered (R) class come back to susceptible (S) (essentially, this would be people who left Facebook changing from "I'm never going back" to "I might go back someday"), or you can have new people come into the population (this would be little Timmy and Claire getting their first computers).
Unfortunately, the authors didn't fit those models. This is, incidentally, a widespread problem in mathematical modeling. A statistical model is an attempt to describe the patterns of variables and their interactions within the data. A mathematical model is an assertion about reality. You can get a SIR model to fit lots of things, but your choice of a SIR model is also an assertion about the system. Namely, that once it peaks, it's heading to zero.
Incidentally, Internet companies do use user-retention models that look a heck of a lot like epidemic models, but they're also considerably more complex than the one presented in the paper.
A: Google Trend in my opinion can't produce a good data set for this case of study. Google trend shows how often a term is searched with Google so there are at least two reasons for raising some doubts about the prevision:


*

*We don't know if the user searches on Google Facebook to log in or if he searches information about Facebook
Facebook is not only a site is a phenomenon, with many articles, books and a film about it and Facebook Inc. on May 18, 2012 began selling stock to the public and trading on the NASDAQ. Google Trend shows you both: the searches for the site and the searches for the "phenomenon". New things always have a great impact to the mass, TV had a great impact to the mass now no one write articles about it but is still one of the most used appliance.


*

*Most users don't search "facebook" on Google to login
With mobile applications and Bookmarks a user with a decent knowledge of internet search "facebook" on Google only the first time then he usually saves the page as a bookmark or download the application. The graph below is the Google trend for Wikipedia, it seems that we will not use Wikipedia in the future. Obviously this is not true we simply don't access to wikipedia typing "wikipedia" we simply search and then use the wikipedia page or we use the bookmark to access to it. 
 
A: A few basic issues stand out with this paper:


*

*It assumes correlation of search engine queries about a rising social network with the membership increases. This may have correlated in the past, but may not in the future.

*There are very few new large social networks. You can almost count them on one hand. Friendster, Myspace, Facebook, Google+. Also, Stack Exchange, Tumblr, and Twitter function similarly to social networks. Is anyone predicting Twitter is over? Quite to the contrary, it seems to have major momentum. There is not much mention or study of other ones to see if they fit. In a way we are talking about, does a trend exist among 5-7 data points? (The number of social networks.) It's just too little data to make any conclusion about the future.

*Facebook displaced Myspace. That was the chief dynamic. It doesn't consider the idea that one infection is displacing another, it tends to consider them separately. What is displacing Facebook? Google+? Twitter? The interaction and "defection" of customers from one "brand" or "product" to the other is the critical phenomenon in this area.

*Social networks coexist. One can be a member of multiple sites. It is true that members may tend to prefer one over the other.

*It would seem a much better model is that there is a consolidation going on, like in economics, such as with automobiles, radio makers, web sites, etc. As in any new disruptive technology, there are many competitors in the beginning, and then, later, the field narrows, they tend to consolidate, there are buyouts and mergers, and some die out in the competition. We already see examples of this, e.g. Yahoo buying out Tumblr recently.

*A similar concept might be with television networks consolidating and being owned by large conglomerates, e.g. major media companies owning many media assets. Indeed, Myspace was bought out by News Corporation.

*The way to go is to look for more analogies between economics and infections (biology). Companies acquiring customers from competitors and the uptake of products do indeed have many epidemiological parallels. There are strong parallels to evolutionary "red queen" races [see the book, Red Queen by Ridley]. There might be connections to a field called bionomics.

*Another basic model is products that compete with each other and have various "barriers to entry" for customers to switch from one brand to another. It is true the cost of switching is very low in cyberspace. It's similar to brands of beers competing for customers, etc.

*In an asymptotic model, it is much more likely that a network increases its members toward some asymptotic maximum and then it tends to plateau. Early in the plateau, it will not be apparent that it is a plateau.
That all said, I think it has some very valid and engaging ideas and is likely to spur much further research. It's groundbreaking, pioneering, and it just needs to be adjusted a bit in its claims. I am delighted in this use of Stack Exchange and collaborative wisdom/collective intelligence analyzing this paper. (Now if only reporters researching the subject would read this whole page carefully before preparing their simplistic sound bites.)
A: My primary concern with this paper is that it focuses primarily on Google search results. It is a well-established fact that smartphone use is on the rise (Pew Internet, Brandwatch), and traditional computer sales are declining (possibly just due to old computers still functioning) (Slate, ExtremeTech), as more people use smartphones to access the internet. Considering there is a native Facebook app for (at least) iOS, Android, Blackberry, and Windows Phone, it's no surprise that the number of Google queries for "facebook" has fallen significantly. If users no longer need to open a browser and mistype "facebook.com" in the URL bar, then that would definitely negatively impact the number of searches. In fact, the number of FB users who use the app has gone up significantly (TechCrunch, Forbes).
I think this study is just some "huh, interesting correlation" that got taken too far by alarmist media outlets; "Did you know the world is changing? How unexpected!"
A: If we take a look at the map of social networks, there are some cases 
that epidemic model applies. 
http://vincos.it/world-map-of-social-networks/
The article could have some other examples (Friendster and Orkut are a good example of massive declination of its users) and also taking into account the fact that normally
people migrate to other social network that offers better or new services.
Facebook inovates the way people comunicate.
Comparing with Orkut, an user needed to enter another person profile to see their updates. On the other hand 
on facebook the feeds are now on his own timeline.
That's a major change.

This model and logic may have worked for MySpace, but is it valid for
  any social network?

IMHO, people don't leave Social Network. They migrate, based on a better service, functionality or experience. 
The question is: Will there be a better Social Network ? Maybe Google +.
A: The answers here are excellent in picking apart the paper's weaknesses; I especially enjoyed @Fomite's critique of their use of SIR models. But it's now been 8 years since this question was asked, and 2017 has come and gone. So I thought it would be fun to revisit this and ask: what do the data show?
Well, facebook user activity data show conclusively that the prediction failed.
First, the number of active monthly users (i.e. users who have logged into their accounts within the last 30 days) has increased fairly steadily. It's levelled off a bit since 2021, but not decreased:

The same picture is true for the number of active daily users, except there's less sign of levelling off [note: the time ranges are slightly different in the two plots]. It's interesting to see a small but notable jump at the beginning of the pandemic that seems to have subsided earlier this year.

[Both images are from Statista, and the links above take you to the page with the latest data]
Bottom line: we already had good explanations for why the prediction was likely to be poor, and we now know it was wrong.
