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Created in 2006, Twitter is an online social networking service in which users share and read 140-character messages called Tweets. The site has approximately 288 million monthly active users who produce about 500 million Tweets per day. This study applies dynamical and statistical modeling strategies to quantify the spread of information on Twitter. Parameter estimates for the rates of infection and recovery are obtained using Bayesian Markov Chain Monte Carlo (MCMC) methods. The methodological strategy employed is an extension of techniques traditionally used in an epidemiological and biomedical context (particularly in the spread of infectious disease). This study, which addresses information spread, presents case studies pertaining to the prevalence of several “trending” topics on Twitter over time. The study introduces a framework to compare information dynamics on Twitter based on the topical area as well as a framework for the prediction of topic prevalence. Additionally, methodological and results-based comparisons are drawn between the spread of information and the spread of infectious disease.