Stochastic model of rumor propagation dynamics on homogeneous social network with expert interaction and fluctuations in contact transmissions

Abstract

The study of uncertainty and its effect on information diffusion have become a recent problem in social network analysis. Contact rates between the social network users are not constant. There exist uncertainty in user’s interest due to incomplete knowledge about others and stochastic properties present in user behavior. Keeping given this fact, we introduce a rumor model in a homogeneously mixed population on a social network including expert intervention. We also studied the stochastic version of the proposed model including fluctuations in contact rates. We ascertained a threshold known as basic influence number, R0 and R0 for deterministic and stochastic model respectively. We acquired the condition of local and global asymptotic stability of rumor free equilibrium respectively for the deterministic and stochastic model. Moreover, the mathematical state of epidemic invasion was obtained for the stochastic version of the model. Here, we conclude that epidemic can still grow in the presence of fluctuations (R0>1) even when there is no epidemic invasion in the deterministic case (R0<1). So a diffusion rate can be a cause of transient epidemic advance.