Modeling collective blogging dynamics of popular incidental topics

Abstract

An extended susceptible-infective (SI) epidemic model is presented in this paper to describe the collective blogging behavior on popular incidental topics. Our model has two major extensions over the classic SI model: in the new model, different blog writers get interested in a specific topic with different probabilities, while in a classic SI model, the infection probability of a disease between any two individuals is identical; the new model takes into consideration the impact of external mainstream media on blog writers, while in a classical SI model, spreading of diseases is merely based on personal contacts between individuals. The new model is capable of explaining the widely observed early burst and heavy tail of topic propagation velocity. The proposed model has a closed-form solution when the individual interest is of uniform distribution with the external influence assumed constant. We validate the proposed model using ten topics from two different data sets: Sina Blog and LiveJournal Blogspace, the results indicating that our model fits the topic propagation velocity and predicts the propagation trend very well.