It is of great practical significance to figure out the propagation mechanism and outbreak condition of rumor spreading on online social networks. In our paper, we propose a multi-state reinforcement diffusion model for rumor spreading, in which the reinforcement mechanism is introduced to depict individual willingness towards rumor spreading. Multiple intermediate states are introduced to characterize the process that an individual's diffusion willingness is enhanced step by step. We study the rumor spreading process with the proposed reinforcement diffusion mechanism on two typical networks. The outbreak thresholds of rumor spreading on both two networks are obtained. Numerical simulations and Monte Carlo simulations are conducted to illustrate the spreading process and verify the correctness of theoretical results. We believe that our work will shed some light on understanding how human sociality affects the rumor spreading on online social networks.
In this paper, we propose a heterogeneous multi-stage model to study the effect of social reinforcement on information propagation. Both heterogeneity of network components and the heterogeneity of individual reinforcement thresholds are considered. An information outbreak condition is derived, according to which the outbreak scale and individual density of each state under specific propagation parameters can be deduced. Monte Carlo experiments are conducted in Facebook networks to demonstrate the outbreak condition, and we find that social reinforcement effects generally inhibit the propagation of information though it contributes to the emergence of certain hot spots simultaneously. Additionally, by applying Pontryagin's Maximum Principle, we derive the optimal control strategy in the case of limited control resources to maximize the information propagation. Then the forward-backward sweep method is utilized to verify its performance with numerical simulation.
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