Dynamics of a Rumor Propagation Model With Stochastic Perturbation on Homogeneous Social Networks

The rapid development of information society highlights the important role of rumors in social communication, and their 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. First, a unique global positive solution of the rumor propagation model is obtained. Then, we verify that the extinction and persistence of the stochastic rumor propagation model are restricted by some conditions. If $R̂0*<1$ and the noise intensity $σi(i=1,2,3)$ satisfies some certain conditions, rumors will extinct with a probability one. If $R0*>1$⁠, rumor-spreading individuals will persist 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. The numerical results show that (1) on the premise that other parameters are determined, the increase of noise intensity can effectively control the spread of rumors; (2) cut off the way of spreading rumors and reduce the contact between ignorant and rumor-spreading individuals (i.e., reduce the value of α); popularize scientific knowledge, reducing the attraction of rumors (i.e., increase the value of β) or replacing rumors of emergencies with other hot topics (i.e., increase the value of η) can effectively curb rumor propagation.