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How Infectious Was #Deflategate? Megan Eberle University of Wisconsin-La Crosse, [email protected]

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How Infectious Was #Deflategate? Megan Eberle University of Wisconsin-La Crosse, Eberle.Megan@Uwlax.Edu Spora: A Journal of Biomathematics Volume 1 | Issue 1 Article 5 2015 How Infectious Was #Deflategate? Megan Eberle University of Wisconsin-La Crosse, [email protected] Eric A. Eager University of Wisconsin-La Crosse, [email protected] James Peirce University of Wisconsin-La Crosse, [email protected] Follow this and additional works at: https://ir.library.illinoisstate.edu/spora Part of the Applied Mathematics Commons Recommended Citation Eberle, Megan; Eager, Eric A.; and Peirce, James (2015) "How Infectious Was #Deflategate?," Spora: A Journal of Biomathematics: Vol. 1: Iss.1, . DOI: https://doi.org/10.30707/SPORA1.1Eberle Available at: https://ir.library.illinoisstate.edu/spora/vol1/iss1/5 This Mathematics Research is brought to you for free and open access by ISU ReD: Research and eData. It has been accepted for inclusion in Spora: A Journal of Biomathematics by an authorized editor of ISU ReD: Research and eData. For more information, please contact [email protected]. How Infectious Was #Deflategate? Megan Eberle1, Eric Eager1,*, James Peirce1 *Correspondence: Abstract Prof. Eric Eager, In mid-January 2015 the National Football League (NFL) started an investigation into Dept. of Mathematics, UWL whether the New England Patriots deliberately deflated the footballs used during their AFC 1725 State St., La Crosse, WI Championship win. Like an infectious disease, the initial discussion regarding Deflategate 54601, grew rapidly on social media sites in the days after the release of the story, only to slowly USA dissipate as interest in the NFL waned following the completion of its season. We apply a [email protected] simple epidemic model for the infectiousness of the Deflategate news story. We find that the infectiousness of Deflategate rivals that of many of the infectious diseases that we have seen historically and is actually more infectious than recent news stories of seemingly greater cultural importance. Keywords: disease model, inverse problem, national football league, basic reproduction num- ber 1 Introduction tween 12.5 and 13.5 pounds per square inch. Deflated footballs would have given the Patriots a competitive The National Football League (NFL) has made Ameri- advantage over the Colts (as well as other opponents) can football arguably the most popular sport throughout by allowing them to exploit the differences between an the United States. The NFL was formed in 1922 from improperly-inflated football and a properly-inflated foot- the American Professional Football Association and orig- ball [7]. inally consisted of 18 teams. By 1925 the league began Discussion regarding Deflategate was sparked in- drawing tens of thousands of fans into stadiums to watch stantly on social media and grew rapidly in the hours and games live, and by 1934 the first NFL game between days after the release of the story. The scandal gained na- the Chicago Bears and the Detroit Lions on Thanksgiv- tional attention quickly as the New England Patriots had ing Day was broadcasted live on national radio|allowing just earned a trip to Super Bowl XLIX against the Seattle the league's fan base to spread nationally. As the radio Seahawks (another team displaying questionable ethics of and television became more widespread across the United its own in previous seasons [14]). Since the Super Bowl is States, the NFL was able to increase their popularity as the most anticipated game in the NFL season, attention almost all NFL games were broadcasted on radio or tele- to the story was heightened. After the Super Bowl was vision by 1964, allowing professional football to overtake over, the scandal slowly began to dissipate and lost much professional baseball in popularity around 1965. The pop- of the attention it originally had, as interest in the NFL ularity of the NFL continues to grow today as television decreased at the completion of its season. This interest ratings surge into the millions viewers and stadiums grow continued to dissipate until early May 2015, when the to house over 100,000 fans [13]. aftermath of a 243-page report by independent attorney Despite the popularity of the NFL, its history has been Theodore V. Wells, Jr., resulted in the NFL suspending plagued by numerous scandals, with the most recent scan- Patriots star quarterback Tom Brady for the first four dal involving the footballs used by the New England Pa- games of the 2015 season and stripping the team of two triots in the 2015 AFC Championship game against the high draft picks. In early September this suspension was Indianapolis Colts, which has become known as “Deflate- nullified, allowing Brady to play the entire 2015 season gate". On Monday January 19, 2015, a story broke that [4]. the NFL had started an investigation into whether the The sharp rise in interest in the Deflategate scandal New England Patriots deliberately deflated the footballs and then an initial slow dissipation of interest is similar they used during their AFC Championship win over the to that of an outbreak of an infectious disease. When an Indianapolis Colts. The NFL rules state that footballs infectious disease is first introduced to a new population, must weigh between 14 and 15 ounces and be inflated be- it can spread rapidly as a large number of the popula- 1Department of Mathematics, University of Wisconsin-La Crosse, La Crosse, WI www.sporajournal.org 2015 Volume 1(1) page 28 How Infectious Was #Deflategate? Eberle, Eager, Peirce tion becomes infected with the disease. As more of the 2 The Model susceptible population becomes infected with the disease, the number of possible interactions between susceptible While the punishment of the Patriots in May 2015, and and infectious individuals, and thus the rate of new infec- the subsequent lift of said punishment in September 2015, tions, decreases. The infectiousness of a disease can often created their own news stories regarding Deflategate, we be captured by a dimensionless parameter called the basic will consider only the dynamics of the initial story, oc- reproduction number R0. The value of R0 is the expected curring in January 2015. We assume that information number of secondary cases produced by a single infected concerning Deflategate is spread person to person like an individual when introduced to a completely susceptible acute infection. We will focus on the subpopulation of population. For example, the R0 value for the 2014 out- media consumers that use the social media site Twitter. break of Ebola virus in West Africa estimated between Time t will be measured in days since the first report of 1.51 and 2.53 [1], meaning that if one person was infected Deflategate on January 19th, 2015. Using the terminol- with Ebola during the early stages of the epidemic, they ogy of Kermack and McKendrick [20] we categorize the would likely spread the virus to approximately 2 other individuals in the Twitter population as susceptible, in- people before they recovered or died. Some other R0 val- fectious, and removed. The susceptible population S(t) ues include 4 for the HIV and SARS, 10 for mumps and (measured in thousands) are those individuals that reg- 18 for measles [12]. An R0 value of 18 is extremely high ularly read and comment on sports news but have yet and means that measles is extremely infectious, which is to comment on Deflategate as of time t. The infectious why the disease is so catastrophic when it persists within population I(t) (measured in thousands) are those that a population. are tweeting (or retweeting) posts about Deflategate us- ing the keywords #deflategate, deflate gate, deflate-gate, Since the spread of the Deflategate scandal appears spygate, or “deflated balls" (chosen to match available to be similar to an infectious disease, we compute the data). As a simplifying assumption we consider each R0 value for this news event in order to quantify the tweet as representing a unique individual (tweeter), and story's infectiousness. To do this we must determine a thus tweets and individuals in the infectious class are useful medium through which information was spread, In discussed interchangeably. The removed population R(t) this paper, we use the the social networking site Twitter (measured in thousands) includes either those individu- (http://twitter.com). Twitter allows users post tweets, als who do not read or comment on sports (and are hence a message under 140 characters, to their Twitter page so removed from this news event even from the very begin- that their followers, other users who will see the tweet, ning), or individuals that were once tweeting about the can read their message. The followers can then reply to story and have permanently stopped using the Deflate- the message and start a conversation with the owner of gate keywords. Due to the short lifespan of the story the tweet. They can also retweet that tweet to their fol- (on the order of weeks), we assume that the immigra- lowers. A retweet is when follower takes a tweet they saw tion of new users and emigration of current users can be and posts it onto their Twitter page for their followers neglected, yielding a constant total population size. to see. The number of tweets and retweets about De- The progression from the susceptible population S to flategate can be used to determine the R0 value and the the infectious population I to the recovered (or maybe infectiousness of this scandal as a news story. more appropriately named bored) population R can be visualized in the traditional SIR conceptual diagram (Fig- In this paper we utilize a simple SIR epidemic model ure 1). The progression of the information through the for the infectiousness of the NFL's Deflategate news story. population depends on many factors. One of the most We then use Twitter data to estimate the parameters of prominent is the total number of \interactions" between this model using standard techniques from the study of susceptible and infectious individuals.
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