Global stability of a rumor spreading model with discontinuous control strategies

With the rapid development of online media in recent years, rumors have also proliferated and spread. If they are not effectively managed, they will cause great harm to society. So, how to stop the spread of rumors has become a hot topic that needs to be studied. In this study, we consider a rumor spreading model with discontinuous control strategies. According to differential inclusion theory, we investigate the existence and boundedness of the solution of the model. By the theory of topological degree, we derive some conditions for the existence of the equilibria of the model, as well as studying the global asymptotic stability of the rumor-free equilibrium and the positive equilibrium. Finally, we study global convergence in finite time. These findings can aid in the development of rumor-control policies. The study may have important implications for effectively predicting and preventing rumor spread.(c) 2022 Elsevier B.V. All rights reserved.