Dynamic analysis and immune control strategy of a rumor propagation model considering network topology

This study constructs a rumor propagation model based on complex networks to investigate how the network topology and the initial distribution of different types of disseminators influence the rumor spreading process. To analyze the model's dynamic behavior, we first solve for its equilibria. Subsequently, the basic reproduction number is derived using the next-generation matrix method. To investigate the mechanisms of rumor propagation, we conduct simulations on a BA scale-free network. This allows us to explore the impact of key parameters and perform a sensitivity analysis on the basic reproduction number. Three different strategies for positioning the initial disseminators are established to analyze their effect on the dynamics of rumor spread. For our proposed model, we adopt random and target immunization strategies and derive the corresponding basic reproduction numbers. The simulation results demonstrate that the placement of initial disseminators in the network core significantly influences rumor dynamics. When a rumor disseminator is located in the core area, both the propagation rate and the scope of influence increase markedly. Conversely, positioning a truth disseminator in the core effectively suppresses rumor spread.