Rumor Spreading Model Considering Individual Activity and Refutation Mechanism Simultaneously

With the rapid development of social networks, an increasing number of factors will affect the spread of rumors. In this paper, we simultaneously consider individual activity differences and rumor-refuting nodes, and we propose a new multifactor model that can be used to better analyze the process of rumor spreading in practice. The equilibrium point and the basic regeneration number R0 of the model are calculated via the differential dynamics method and the next generation matrix method. Moreover, the local asymptotic stability of the equilibrium of the model is determined based on the Routh-Hurwitz criteria. The global stability is proved via the geometric method which is based on the use of a higher-order generalization of Bendixson's criterion. Finally, the theoretical results are verified via numerical simulation in a homogeneous network, and the effects of individual activity and the refutation mechanism on the rumor spreading process are analyzed. We find that the proposed mechanism of rumor refutation can effectively reduce the density of spreaders and the rumor duration.