Social networks are an important infrastructure for information, the paper present a information diffusion model with random perturbation in social networks, which is based on SIR deterministic epidemic diseases. We prove that there exists a unique nonnegative solution to the stochastic information diffusion model for any positive initial value, investigate the stochastic asymptotic behavior of the information diffusion model, give the stability condition by the construction of the Lyapunov function, i.e. the conditions of the information diffusion will die out and be persistent in social networks.
Abstract. The paper explore an information diffusion models with random perturbation in social network. First, we show the models exit the unique global positive solution. By the construction of the Lyapunov function, we give the positive solution is stochastically asymptotically stable in the large around disease-free equilibrium, i.e. the conditions of the information diffusion will die out, investigate the stochastic asymptotic behavior of the positive solution around endemic equilibrium of the deterministic models, obtain the stochastic asymptotic stability condition, i.e. the conditions of the information diffusion will be persistent in social networks.
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