Dynamic Analysis of a Stochastic Rumor Propagation Model with Regime Switching

Abstract

We study the rumor propagation model with regime switching considering both colored and white noises. Firstly, by constructing suitable Lyapunov functions, the sufficient conditions for ergodic stationary distribution and extinction are obtained. Then we obtain the threshold Rs which guarantees the extinction and the existence of the stationary distribution of the rumor. Finally, numerical simulations are performed to verify our model. The results indicated that there is a unique ergodic stationary distribution when Rs>1. The rumor becomes extinct exponentially with probability one when Rs<1.