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Rumors have been widespread with the development of self-media, which has brought new challenges to government departments in dealing with rumor management. Considering the combined effect of the external refutation of media reports and the internal refutation of the counter individuals, the susceptible-infective-counter-media-remover (SICMR) rumor propagation model with a double refutation mechanism is proposed. The two thresholds for rumor propagation are obtained by mathematical analysis of the model. Based on the Jordan matrix theory and Routh-Hurwitz judgment, two rumor-free equilibriums (RFE) and four rumor-spread equilibriums (RSE) are obtained, and the stability of the equilibria is proved. The theoretical results and the influence of key parameters are verified by numerical simulation, and the validity of the model is verified through comparative experiments. Using the simulation data for function fitting, the results showed that the initial values of the media reports and the counter individuals are exponentially related to the peak of rumor propagation, respectively. Finally, based on two real rumor datasets of Twitter, the least square method is used to fit the model parameters. Through the comparison experiment with other similar works, the R-squared of the SICMR is 0.8811 and 0.9469 on two real datasets, respectively, which is the best result. [ABSTRACT FROM AUTHOR]