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Social media is being increasingly used as a political communication channel. The web makes it easy to spread extreme opinions or ideologies that were once restricted to small groups. Terrorists and extremists use the web to deliver their extreme ideology to people and encourage them to get involved in fanatic behaviors. In this research, we aim to understand the mechanisms and properties of the exposure process to extreme opinions through these new publication methods, especially web forums. We propose the topic diffusion model for web forums, based on the SIR (Susceptible, Infective, and Recovered) model frequently used in previous research to analyze disease outbreaks and knowledge diffusion. The logistic growth of possible authors, the interaction between possible authors and current authors, and the influence decay of past authors are incorporated in a novel topic-based SIR model. From the proposed model we can estimate the maximum number of authors on a topic, the degree of infectiousness of a topic, and the rate describing how fast past authors lose influence over others. We apply the proposed model to a major international Jihadi forum where extreme ideology is expounded and evaluate the model on the diffusion of major violent topics. The fitting results show that it is plausible to describe the mechanism of violent topic diffusion in web forums with the SIR epidemic model.