Global Stability of the Endemic Equilibrium of a Stochastic Information Diffusion Model in Social Networks Based on Epidemic Model

Abstract

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.