Dynamic Analysis of a Stochastic Rumor Model with Media Coverage and Whistleblowing Mechanism

Considering the influence of whistleblowing mechanism and media coverage, a novel stochastic rumor propagation model along with stochastic disturbance is proposed in this article. Firstly, the existence of a global positive solution is proved by defining the stop time. Secondly, sufficient conditions of the extinction and persistence are derived by means of the strong law of large numbers and Itô's formula. Finally, numerical simulations indicate that the effectiveness and rationality of the model.