Mathematical Biosciences and Engineering (MBE)

Modeling the impact of twitter on influenza epidemics

Pages: 1337 - 1356, Volume 11, Issue 6, December 2014      doi:10.3934/mbe.2014.11.1337

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Kasia A. Pawelek - Department of Mathematics and Computational Science, University of South Carolina Beaufort, Bluffton, SC 29909, United States (email)
Anne Oeldorf-Hirsch - Department of Communication, University of Connecticut, Storrs, CT 06269, United States (email)
Libin Rong - Department of Mathematics and Statistics, Oakland University, Rochester, MI 48309, United States (email)

Abstract: Influenza remains a serious public-health problem worldwide. The rising popularity and scale of social networking sites such as Twitter may play an important role in detecting, affecting, and predicting influenza epidemics. In this paper, we develop a simple mathematical model including the dynamics of ``tweets'' --- short, 140-character Twitter messages that may enhance the awareness of disease, change individual's behavior, and reduce the transmission of disease among a population during an influenza season. We analyze the model by deriving the basic reproductive number and proving the stability of the steady states. A Hopf bifurcation occurs when a threshold curve is crossed, which suggests the possibility of multiple outbreaks of influenza. We also perform numerical simulations, conduct sensitivity test on a few parameters related to tweets, and compare modeling predictions with surveillance data of influenza-like illness reported cases and the percentage of tweets self-reporting flu during the 2009 H1N1 flu outbreak in England and Wales. These results show that social media programs like Twitter may serve as a good indicator of seasonal influenza epidemics and influence the emergence and spread of the disease.

Keywords:  Mathematical model, epidemiology, stability, Hopf bifurcation, influenza, social media, twitter, data fitting.
Mathematics Subject Classification:  Primary: 92D25, 92D30; Secondary: 34D20, 34C23, 91C99.

Received: December 2013;      Accepted: June 2014;      Available Online: September 2014.