A Stochastic Information Diffusion Model in Complex Social Networks

The number of potential participants in information diffusion is dynamically changing, and the topological structure of a real social network is affected by environment noise. In this paper, a stochastic information diffusion model considering both population perturbation and connectivity variation has been proposed. For the model on homogeneous network, we show the existence and uniqueness of the global positive solution and give a sufficient condition of extinction of information. A series of numerical simulations on Watts-Strogatz (WS) network, Barabási-Albert (BA) network and real-world Facebook network have been conducted to verify the theoretical analysis and evaluate the sensitivity of the proposed model to relevant parameters. We find that both population perturbation and connectivity variation have great impacts on information diffusion process. In general, the connectivity variation noise promotes the spread of information, and the population perturbation noise corresponding to I-infected individuals inhibit the spread of information. In the case of large noise intensity, the population perturbation noise corresponding to I-infected individuals plays a decisive role compared with the connectivity variation noise.