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With the rapid growth of mobile devices, the platform of online social networks plays a prominent field for information spreading whether they are objective facts or fake news. To some degree, it can enable people to obtain more information faster and easier than before. However, the dynamical process of different information diffusion may generate different social influence. Especially, the negative information spreading may lead to economic losses or bring a serious social security threat. To explore the same information diffusion to different aspects, we propose an information propagation model SFTRD based on heterogeneous OSNs. SFTRD model not only considers the evolution of the same information, and also considers how to block the negative information spreading widely. Based on the theoretical analysis, the stability of equilibrium is performed by suitable analytical methods. The global asymptotic stability of the endemic equilibrium is studied by a geometric approach. The restrain strategies of spreading truth or blocking negative information are discussed by the optimal control theoretical. An optimal control method of SFTRD model is formulated, which minimizes the rumor-restraining cost within an expected time period. To validate the theoretical analysis of the proposed model, a set of numerical experiments are carried out with different parameter settings. Based on the theoretical analysis and numerical experiments, we can find that the process of information propagation is affected by various factors and we should explorer different inhibition strategies. • We established an information propagation model in heterogeneous networks. • Global and local stability analyses of equilibrium are performed by suitable analytical methods. • An optimal control strategy of the proposed SFTRD model is studied. • We carried out a series of numerical experiments to validate the proposed model. [ABSTRACT FROM AUTHOR]