Stochastic asymptotically stability of an Information Diffusion Model with Random Perturbation in Social Network

Abstract

The paper explore a information diffusion models with random perturbation in social network. The information diffusion stochastic models are established by using stochastic differential equation, by the Lyapunov method, the long time behavior of the stochastic systems is studied. If the basic reproduction number is not more than 1, a sufficient condition that the disease-free equilibrium of the information diffusion system is stochastic asymptotically stable in the large is given, i.e. the conclusion implies that information diffusion will vanish. If the basic reproduction number is greater than 1, a sufficient condition that the endemic equilibrium of the information diffusion system is stochastic asymptotically stable in the large is given, i.e. the result implies that the information diffusion will be persistent in social networks.