Source-linked AI summary
Epidemiological modeling of online social network dynamics
John Cannarella, Joshua A. Spechler
TL;DR
The paper asks how to model OSN adoption and abandonment when the traditional SIR recovery assumption may not fit user behavior. It modifies SIR recovery to depend on contact with recovered members and fits the model to Google query data. The model fits MySpace better than traditional SIR and projects a rapid Facebook decline, though the projection is especially uncertain on the slower-decline side.
Problem
Traditional SIR recovery assumes a characteristic recovery rate, whereas OSN users may lose interest as their peers do, making abandonment dynamics difficult to represent.
Source: Infectious recovery SIR model · p. 3Method
The paper modifies SIR so recovery requires contact with recovered members and fits model curves to Google search queries used as a proxy for OSN activity.
Source: Infectious recovery SIR model · p. 3, Google Trends Search Query Data · p. 4, Search Query Data Curve Fitting · p. 5Results
The irSIR model reduces MySpace SSE by 75% versus traditional SIR, and its Facebook extrapolation predicts decline to 20% of peak query activity by December 2014.
Source: MySpace · p. 6, Facebook · p. 6, Conclusions · p. 7Takeaways & Limitations
The MySpace fit supports infectious abandonment as a useful description of OSN dynamics, while the Facebook projection suggests rapid decline in the coming years.
Source: MySpace · p. 6, Conclusions · p. 7Facebook’s decline is dictated by post-2012 data, leaving a wide range of slower-declining trajectories consistent with the fit.
Source: Facebook · pp. 6–7
Abstract
from arXiv · showhide
The last decade has seen the rise of immense online social networks (OSNs) such as MySpace and Facebook. In this paper we use epidemiological models to explain user adoption and abandonment of OSNs, where adoption is analogous to infection and abandonment is analogous to recovery. We modify the traditional SIR model of disease spread by incorporating infectious recovery dynamics such that contact between a recovered and infected member of the population is required for recovery. The proposed infectious recovery SIR model (irSIR model) is validated using publicly available Google search query data for "MySpace" as a case study of an OSN that has exhibited both adoption and abandonment phases. The irSIR model is then applied to search query data for "Facebook," which is just beginning to show the onset of an abandonment phase. Extrapolating the best fit model into the future predicts a rapid decline in Facebook activity in the next few years.
Introduction
Online social networks can rise and fall rapidly, making their dynamics important both academically and financially. The paper applies epidemiological models to adoption and abandonment and uses Google search queries as a proxy for OSN usership.
Introduction
- MySpace’s rise and collapse show why OSN dynamics matter financially as well as academically.It peaked at 75.9 million unique monthly US visits in 2008, then declined to obscurity by 2011; its 2011 sale followed a $580 million purchase in 2005.Source: Introduction · p. 1
- The paper models OSN adoption and abandonment by analogy to infectious disease spread.Users may join because their friends have joined, while loss of interest is likened to gaining immunity.Source: Introduction · p. 1
- Public Google search queries provide a proxy for OSN usership, which is difficult to measure directly.The paper builds on prior use of search queries as proxies for quantities such as flu cases.Source: Introduction · pp. 1–2
Model
The paper maps the classical SIR compartments to OSN users and revises recovery so abandonment spreads through contact with people who have left or resist joining. This makes an initial recovered population necessary and implies eventual decline when that population is nonzero.
Traditional SIR model
- The traditional SIR model uses susceptible, infected, and recovered compartments whose sizes sum to a constant population N.This constant-population assumption is described as valid for outbreaks short relative to members’ lifespans.Source: Traditional SIR model · p. 2
- Traditional SIR infection depends on contact between susceptible and infected populations, whereas recovery is proportional to I and does not require compartment contact.The equations can be solved numerically with initial values S(0), I(0), and R(0); I(0) must be nonzero for infection to spread.Source: Traditional SIR model · p. 2
- In the OSN analogy, susceptible people could join, infected people are users, and recovered people have left or resist joining.The recovered compartment can include people with no intention of returning to the network.Source: Traditional SIR model · p. 3
Infectious recovery SIR model
- In the irSIR model, recovery depends on contact with the recovered population, reflecting abandonment that spreads as users’ peers lose interest.The recovered fraction is incorporated into the recovery terms, replacing the traditional model’s characteristic recovery rate.Source: Infectious recovery SIR model · p. 3
- The irSIR immunization criterion can stop growth, but the model provides no analogous way to immunize users against recovery.The paper concludes that R increases over time whenever R0 is nonzero.Source: Infectious recovery SIR model · pp. 3–4
- With any nonzero initial recovered population, the irSIR model has no way to prevent recovery and therefore expects OSNs eventually to decline.If R0 is zero, no infected members recover; the model therefore requires a small initial recovered compartment.Source: Infectious recovery SIR model · pp. 3–4
Methods
The methods use Google Trends queries as a measure of OSN activity, adjust and normalize weekly data, and fit epidemiological model curves by minimizing squared error. Facebook’s October 2012 query jump is treated as an artifact, while MySpace and Facebook query histories are compared with reported activity timelines.
Google Trends Search Query Data
- Google Trends query frequency is used as a proxy for OSN activity, capturing web traffic and interest rather than inactive registered accounts.The data are publicly available, while historical OSN user activity data are typically proprietary and difficult to obtain.Source: Google Trends Search Query Data · p. 4
- Weekly query values are normalized so the selected period’s maximum equals 100, and overlapping time segments are rescaled to increase resolution.Weekly rather than daily data avoid day-of-week variation in search activity.Source: Google Trends Search Query Data · p. 4
- The Facebook query jump in early October 2012 is treated as an artifact possibly associated with Google’s Penguin 3 update.The paper removes it by multiplying subsequent data by 0.804, based on the assumption that a reporting artifact would affect queries proportionally.Source: Google Trends Search Query Data · pp. 4–5
- MySpace’s query curve follows its reported rise and fall, while Facebook’s decline from 2013 accords with reports of younger users leaving.The curves cross near April 2008, when Facebook reportedly overtook MySpace in global web traffic.Source: Google Trends Search Query Data · p. 5
Search Query Data Curve Fitting
- The model’s infected-population curve is fitted to weekly query data by minimizing sum of squared error over five input parameters.The fitting procedure uses MATLAB’s fminsearch with a Nelder–Mead simplex method and a Dormand–Prince solver.Source: Search Query Data Curve Fitting · p. 5
Results and discussion
The irSIR model fits MySpace search-query data better than the traditional SIR model, and its Facebook fit predicts rapid decline. Facebook forecasts remain sensitive to post-2012 observations and model parameters.
MySpace
- 75% lower SSE: the irSIR model fits MySpace search-query data better than the traditional SIR model, particularly near the curve’s shoulders.MySpace’s full rise-and-fall cycle falls within the available Google Trends period.Source: MySpace · pp. 5–6
- Facebook’s best-fit irSIR forecast projects a rapid decline to 20% of its maximum size by December 2014.The paper defines this threshold as an arbitrary end-of-life date.Source: Facebook · p. 6
- The Facebook prediction bounds show that changes in R0 and ν can trade off decline rate against decline onset while remaining within 15% higher SSE than the best fit.The early bound declines faster but starts later; the late bound declines slower but starts earlier.Source: Facebook · p. 6
- The prediction bounds are asymmetric: slower-than-best-fit decline is more likely, because the decline is dictated by post-2012 data.Without post-2012 observations, a finite-SSE solution with constant Facebook size is possible; faster declines are bounded by the last reported data point.Source: Facebook · pp. 6–7
Conclusions
The paper applies a modified epidemiological model to online social network adoption and abandonment. MySpace results favor infectious recovery over traditional SIR, while the Facebook extrapolation suggests rapid decline.
Conclusions
- A 75% decrease in SSE is achieved by modifying traditional SIR to incorporate infectious recovery dynamics, providing a better description of OSN dynamics.The model is validated on MySpace search-query data before application to Facebook; the extrapolation suggests Facebook will lose 80% of its peak user base between 2015 and 2017.Source: Conclusions · p. 7
Tables
The tables define epidemiological-to-OSN parameter analogues and report model-fitting parameters; accompanying figures visualize normalized MySpace and Facebook query data with model fits.
Tables
- Figure 3 overlays normalized MySpace search-query data with best-fit SIR and irSIR models.The maximum data point is scaled to 100.Source: Figure 3 · p. 10
- Figure 4 overlays Facebook search-query data with the best-fit irSIR model and bounds for decline timing.The bounds correspond to earliest and latest decline times with a 15% increase in SSE over the best fit.Source: Figure 4 · p. 10
- Table 1 defines epidemiological model parameters and their OSN analogues.Source: Table 1 · p. 11, Tables · p. 11
- Table 2 reports parameter values from fitting epidemiological models to search query data.Source: Table 2 · p. 11, Tables · p. 11