Online social networks (OSN) have become one of the major platforms for people to exchange information. Both positive information (e.g. ideas, news and opinions) and negative information (e.g. rumors and gossips) spreading in social media can greatly influence our lives. Previously, researchers have proposed models to understand their propagation dynamics. However, those were merely simulations in nature and only focused on the spread of one type of information. Due to the humanrelated factors involved, simultaneous spread of negative and positive information cannot be thought of the superposition of two independent propagations. In order to fix these deficiencies, we propose an analytical model which is built stochastically from a node level up. It can present the temporal dynamics of spread such as the time people check newly arrived messages or forward them. Moreover, it is capable of capturing people's behavioral differences in preferring what to believe or disbelieve. We studied the social parameters impact on propagation using this model. We found that some factors such as people's preference and the injection time of the opposing information are critical to the propagation but some others such as the hearsay forwarding intention have little impact on it. The extensive simulations conducted on the real topologies confirm the high accuracy of our model.
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