Dynamic analysis of the IFCD rumor propagation model under stochastic disturbance on heterogeneous networks

Abstract

By taking full consideration of the heterogeneity of network users and stochastic disturbance of network environment, a stochastic IFCD (Ignorants-Forwarders-Collectors-Deleters) rumor propagation model is proposed on heterogeneous networks. This study takes MicroBlog as the research background to investigate the dynamical behaviors of rumor spreading on online social networks, which paves the way for controlling rumors effectively and provides positive guidance for the network public opinion. Firstly, some preparations for building a stochastic model are given, including establishing a deterministic IFCD rumor propagation model and obtaining the rumor-free/spreading equilibrium. Secondly, considering the impact of stochastic disturbance on rumor propagation, the corresponding stochastic rumor propagation model is established. Thirdly, a stopping time is defined, which manifests the existence of the unique global positive solution in the stochastic model. Next, sufficient conditions of the rumor extinction and persistence are obtained by using Itô’s formula and strong law of large numbers. Additionally, simulations are operated to validate the results. Finally, the application of the model is shown to bear out the applicability of the proposed model.