Stability analysis and optimal control of a rumor propagation model based on two communication modes: friends and marketing account pushing.

In addition to spreading information among friends, information can also be pushed through marketing accounts to non-friends. Based on these two information dissemination channels, this paper establishes a Susceptible-Infection-Marketing-Removed (SIMR) rumor propagation model. First, we obtain the basic reproduction number $ R_0 $ through the next generation matrix.