Competitive spreading model and control strategies of negative emotions and intervention information in heterogeneous social networks

Emotions play an important role in individual decision making, and emotional contagion affects both individual and group-level behaviors. Particularly, in the case of emergencies, the contagion of negative emotions may have an extremely negative impact on the stability of society. However, emergency management is equally likely to take measures during the spread of negative emotions. In this context, we designed a model to discuss the dynamic characteristics of competing propagation of negative emotions and intervention information in heterogeneous social networks. Firstly, the basic reproduction number and propagation threshold for the propagation of negative emotions in the presence of intervening information are calculated based on the existence of the positive equilibrium points. Secondly, the existence and stability of equilibrium points of the model are analyzed based on the theory of infectious disease dynamics, Lyapunov stability and LaSalle’s invariance principle. Thirdly, three different control strategies are investigated, including uniform immunization control, active immunization control and optimal control. Finally, we numerically simulate the proposed model and the relative importance of the different factors contributing to the spread and prevalence of negative emotions is discussed through a sensitivity analysis, which can provide the best strategies for reducing the spread of negative emotions.