Numerous studies have attempted to model the effect of mass media on the transmission of diseases such as influenza, however quantitative data on media engagement has until recently been difficult to obtain. With the recent explosion of "big data" coming from online social media and the like, large volumes of data on a population's engagement with mass media during an epidemic are becoming available to researchers. In this study we combine an online data set comprising millions of shared messages relating to influenza with traditional surveillance data on flu activity to suggest a functional form for the relationship between the two. Using this data we present a simple deterministic model for influenza dynamics incorporating media effects, and show that such a model helps explain the dynamics of historical influenza outbreaks. Furthermore, through model selection we show that the proposed media function fits historical data better than other media functions proposed in earlier studies.