Research on a Rumor Transmission Model with Refutation Mechanism

Abstract

With the refutation mechanism supplemented to the SIR rumor spreading model, a modified rumor transmission model is established, which includes the process of spreader and ignorant converting to stifler when they contact. A detailed qualitative analysis about existence of its solutions and the local asymptotic stability of its equilibria are carried out. Using the theory of limit systems and the Bendixson-Dulac criteria, we obtained the sufficient conditions for the global asymptotic stability of the equilibria. A numerical simulation is carried out to illustrate the feasibility of our main results. The results show that besides of controlling the propagation threshold of rumors, controlling refutation rate and termination rate is also an effective means to restrain the rumor propagation.