Dynamic analysis of a SIDRW rumor propagation model considering the effect of media reports and rumor refuters

Media reports and refutation factors have an important impact on the spread of rumors. At present, most scholars have separately analyzed the effects of media reports and individual refutation on the spread of rumors. It is not common to comprehensively consider the two on the spread of rumors. This paper proposed a SIDRW (Susceptibility–Infection–Refutation–Recovery–Medium) model, which regarded media as a separate subcategory and comprehensively considered the influence of media reports and individual repudiation on rumor propagation. The existence and local asymptotic stability of the equilibrium point of the model are proved by calculation. The results of numerical simulation under the parameters given in this paper show that positive media publicity can reduce the spread of rumors, but cannot prevent the spread of rumors. In the process of spreading, with an increase in the initial value of rumormongers, the duration of rumor spreading decreases, and the time to reach the peak decreases. This is conducive to controlling the spread of rumors.