Stability analysis of a SAIR rumor spreading model with control strategies in online social networks

Abstract

Nowadays rumors spread by virtual identities of people in online social networks. In order to study the influence of forcing silence on spreaders, we propose a rumor propagation model with a silence-forcing function in online social networks. The theoretical analysis of the rumor propagation model reveals the existence of the equilibrium points, the backward bifurcation and the local stability. Meanwhile, by choosing the key parameter and time delay as the bifurcation parameters, we have given some conditions of Hopf bifurcation that are easy to judge. Furthermore, the optimal control is discussed to reduce the frequency of rumor propagation. Finally, numerical simulations are presented to prove the correctness of the theoretical results.