Research on multi-topic network public opinion propagation model with time delay in emergencies

Abstract

In this paper, three multi-topic network public opinion propagation models, including a without time delay model when each group transforms into new topic propagators (model I); a time delay model when potential propagators transform into new topic propagators (model II); and a time delay model when the initial topic propagators transform into new topic propagators (model III), are established and the basic reproductive number with equilibrium points are found. In addition, stability theory is used to analyze the stability of the public opinion eliminating equilibrium point and the public opinion spreading equilibrium point of the three models. Meanwhile, in order to effectively deal with the negative impact of multi-topic public opinion, an optimal control analysis of the multi-topic network public opinion propagation model is carried out. Finally, a simulation analysis is conducted. It is found that the time delay in model II has no effect on the stability of the public opinion equilibrium points, while the influence of the time delay in model III causes the public opinion eliminating equilibrium point and the public opinion spreading equilibrium point to exhibit Hopf bifurcation.