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There are often many kinds of rumors spreading in new media after emergencies; however, the existing studies have focused on the rumors with competition, and little attention has been paid to those with mutual promotion. Therefore the mutual promotion between two rumors and the state transition rules between different groups are first analyzed. Then a 3SI3R model, extending the classical 2SI2R model, and mean-field equations of the proposed model are given. Further, the stability and influence of the mutual promotion on the final size of two rumors in the proposed model are derived. Finally, numerical simulations are carried out to investigate the influence of factors, that is, the mutual promotion, occurrence time differences, and the forgetting rate, on the propagation of two rumors. The results show that the enhancement of the mutual promotion can accelerate propagation of two rumors and enlarge their final size; the increase of forgetting rate helps to decrease the final size of two rumors; the decrease in occurrence time differences can result in a small increase in the final size of the later rumor, and the overall situation of two rumors becomes more difficult to control.

A 3SI3R model for the propagation of two rumors with mutual promotion