How Infectious Was #Deflategate?

On Monday January 19, 2015 a story broke that the National Football League (NFL) had started an investigation into whether the New England Patriots deliberately deflated the footballs they used during their championship win over the Indianapolis Colts. Like an infectious disease, discussion regarding Deflategate grew rapidly on social media sites in the hours and days after the release of the story. However, after the Super Bowl was over, the scandal slowly began to dissipate and lost much of the attention it had originally had, as interest in the NFL wained at the completion of its season. We construct a simple epidemic model for the infectiousness of the Deflategate news story. We then use data from the social media site Twitter to estimate the parameters of this model using standard techniques from the study of inverse problems. We find that the infectiousness (as measured by the basic reproduction number) of Deflategate rivals that of any infectious disease that we are aware of, and is actually more infectious than recent news stories of greater importance - both in terms of the basic reproduction number and in terms of the average amount of time the average tweeter continued to tweet about the news story.

💡 Research Summary

The paper “How Infectious Was #Deflategate?” treats the rapid rise and subsequent decline of public discussion surrounding the NFL’s “Deflategate” scandal as an epidemic process and quantifies its “infectiousness” using a classic SIR (Susceptible‑Infectious‑Removed) model. The authors focus exclusively on Twitter as the transmission medium, defining “susceptible” users as those who follow sports news but have not yet tweeted about the scandal, “infectious” users as those actively posting or retweeting with the keywords #deflategate, “deflate‑gate”, “deflate‑gate”, “spygate”, or “deflated balls”, and “removed” users as those who either never engage or have stopped tweeting about the topic.

The model equations are:
S′(t)=−β S(t) I(t)
I′(t)=β S(t) I(t)−γ I(t)
R′(t)=γ I(t)

Here β is a daily transmission coefficient representing the probability that a susceptible user, upon seeing a relevant tweet, will retweet or create a new tweet, while γ is the recovery (or removal) rate, i.e., the inverse of the average time an individual continues to tweet about the story. The total Twitter population is assumed constant over the short time horizon (≈30 days), allowing the authors to treat S₀+I₀+R₀ as a fixed number.

Empirical data are taken from Topsy, which aggregated the daily count of tweets containing the specified keywords for 30 days after the initial report on January 19, 2015. These daily counts constitute the observed infectious trajectory I(t). The authors model observation error as independent, identically distributed Gaussian noise with zero mean and variance σ², and they employ ordinary least squares (OLS) to estimate the four parameters θ =