This paper proposes a new formal modeling approach to popularity dynamics based on a generic notion of message propagation within society. The approach is demonstrated with two original models of information diffusion. These are a branching model of popularity and a epidemic model of popularity. The first is based on the principles of a branching process, while the second emulates an epidemic equation with a specific infection rate. This allows us to consider the replication phenomena on information diffusion. The approach is validated using a very large dataset collected online that involves keywords in blogs and hashtags on Twitter. Our main results point to an overall good fit of both models, both when the process of popularity grows and when it decays. This is due to endogenous information transfer, as in an epidemic process, but also when the process is initially triggered by an external event. Overall, on balance, our models confirm that popularity builds through message diffusion, which is of the multiplicative kind.

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Branching models,Epidemic models,Information diffusion,Online social media,Popularity dynamics

• Mathematics - Natural Sciences
• Computer and Information Sciences - Natural Sciences
• Sociology - Social Sciences