The Facebook Epidemic

Econintersect:  A curious piece of research by two Princeton University engineering Ph.D. students has compared the growth and decline of disease epidemics to the observed growth and decline of MySpace.  They have projected what the same functional behavior would mean for Facebook.  The results project Facebook losing 80% of its traffic over the next 2-4 years.

The two used an infectious disease model that divides the entire population into three groups:  the susceptible (S), the infected (I) and the recovered (R).  The time rate of change of each group is determined by three differential equations presented in the paper.  The assumption of the model is that the entire population is constant and does not vary over the time frame of the disease.

The study looked at the behavior of Spacebook traffic as represented by Google search queries and fitted the data to SIR model described above.  See the left hand graph below, which Cannella and Spechler characterized as “a poor description of the data“.

The study next observed that a better fit could be obtained using a modified model which assumed that the number of recovered “patients” is proportional to the rate of recovery.  In other words, contact with an already recovered “patient” increases the opportunity for recovery.  This irSIR (ir = infectious recovery) model much better fits the observed MySpace data.  (See right hand graph above.)

The authors discuss the logic supporting the use of the irSIR model:

Eventually, users begin to leave and recovery spreads infectiously as users begin to lose interest in the social network. The notion of infectious abandonment is supported by work analyzing user churn in mobile networks which show that users are more likely to leave the network if their contacts have left.

In 2013 there have been reports that younger users have started to leave Facebook in significant numbers.  This is reflected in the Google search data shown in the graph below.

Cannarella and Spechler caution that the decline in Facebook traffic is entirely dependent on 2013 data and there is no decline forecast using only 2012 and earlier data.  This depends in part on the necessity of a non-zero recovered population to start the “infectious recovery” process there must be some time zero positive non-zero value for R (recovered “patients”) desinated R₀ .  The authors address this as follows:

If R0 were set to 0, none of the infected population would be able to recover since recovery now requires contact with a recovered individual. Mathematically, Equation 3c would be zero for all time, and I would grow at the expense of S until the entire population is infected. In the context of OSN dynamics, R0 can be thought of as the first users to leave the OSN or a compartment of the population that resists joining the OSN altogether. This small initial compartment of OSN resistors is ultimately responsible for the abandonment of the OSN.

In other words, if just a small number of users abandon Facebook then the “infectious recovery” from the “Facebook disease” can commence and the end is “handwriting on the wall”.  The same is true if some part of the population has a natural immunity to Facebook and therefore was never in the susceptible population.

What the Cannarella and Spechler study does not address is the question of mutating disease.

Did MySpace fit the irSIR model by being non-adaptive?  Could Facebook change its operating offering sufficiently that recovered “patients” are again susceptible for infection by the modified “disease”?

Perhaps even more important, can Facebook change its offerings such that the pool of “naturally immune” can now become susceptible?  What is this that we have been hearing about Facebook News, for example?

Econintersect suggests that the day of business plans prepared as pandemic models may just be starting.  Will two engineering students at Princeton end up never doing any Mechanical and Aeronautical Engineering as their career?  Or have these two students merely caught a passing “bug” and will they be in recovery soon as soon as their immune system kicks in?

John Lounsbury

Hat tips to Selva Tinnan and Roger Erickson.

Sources:

• Epidemiological modeling of online social network dynamics (John Cannarella and Joshua A. Spechler, arxiv.org, 17 January 2014)

• Facebook tweaks News Feed algorithm to promote link share posts from Pages over text status updates (Emil Protalinski, TNW Blog, 21 January 2014)