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. Second, we prove that the solutions of the model are uniformly bounded and discuss asymptotically stable of the rumor-free equilibrium point and the rumor-prevailing equilibrium point. Third, we propose an optimal control strategy for rumors to control the spread of rumors in the network. Finally, the above theories are verified by numerical simulation methods and the necessary conclusions are drawn.