Delay differential equations modeling of rumor propagation in both homogeneous and heterogeneous networks with a forced silence function

Abstract

The emergence of rumors is subjective and aggressive which will bring disturbance and misleading to people’s lives. This paper is dedicated to comprehensively investigating the influence of forced silence function, time delay and network topology on rumor propagation in online social networks. Considering the network supervision such as forced silence and network topology, a novel delayed SIR(susceptible-propagating-recovery) epidemic-like rumor propagation model in both homogeneous and heterogeneous networks is proposed. By using the mean-field theory, we analyze the propagation dynamics of the model in detail. Firstly, we demonstrate the boundedness of the solutions, then we obtain the basic reproduction number and the existence of the rumor-prevailing equilibrium points. Secondly, the forward and backward bifurcation as well as the local and global stabilities of the equilibrium points in both homogeneous and heterogeneous networks are theoretically analyzed and revealed. Finally, the possible impact is analyzed through numerical simulations, and the factors affecting rumor propagation are theoretically analyzed, which prove the validity of the theoretical analysis.