Stochastic dynamic effects of rumor propagation on heterogeneous social networks incorporating age-related education and immunity

The advent of mobile social networks has greatly simplified information sharing, yet it has simultaneously increased the risk of rumor propagation. This study examines the dynamics of rumor spreading on platforms such as MicroBlog, with the goal of improving public opinion management. In this paper, an innovative model that considers network heterogeneity, stochastic fluctuations, education age, nonlinear transmission rates, and temporary immunity to study rumor dissemination on complex networks is introduced. Initially, the paper lays out the preparatory steps for developing the stochastic rumor model. Next, it confirms the existence of a unique global positive solution for the model. Following this, the study identifies the conditions necessary for the elimination of rumors. Additionally, the stationary distribution that suggests the persistence of rumors is investigated using Khasminskii’s approach. Finally, simulations and a practical application are carried out to validate the effectiveness of the model.