Abstract
The rapid development of information society highlights the important role of rumors in social communication, and its propagation has a significant impact on human production and life. The investigation of the influence of uncertainty on rumor propagation is an important issue in the current communication study. Due to incomprehension about others and the stochastic properties of the users' behavior, the transmission rate between individuals on social network platforms is usually not a constant value. In this paper, we propose a new rumor propagation model on homogeneous social networks from the deterministic structure to the stochastic structure. Firstly, a unique global positive solution of rumor propagation model is obtained. Then, we verify that the extinction and persistence of stochastic rumor propagation model are restricted by some conditions. IfR *0< 1 and the noise intensity s i (i = 1,2,3) satisfies some certain conditions, rumors will extinct with a probability one. If R *0 > 1, rumor-spreading individuals will continue to exist in the system, which means the rumor will prevail for a long time. Finally, through some numerical simulations, the validity and rationality of the theoretical analysis are effectively verified.