Dynamics and event-triggered control of rumor propagation model with saturated incidence and time delay on heterogeneous networks

Considering the impact of user's cognitive ability in rumor propagation, this paper proposes a new susceptible infection recovery (2SIR) rumor propagation model with saturation incidence and time delay on heterogeneous networks. First, the existence of the equilibria is discussed by using mean field theory and basic reproduction number. Second, the dynamic behaviors of the rumor-free and persistent equilibria are analyzed via the local linearization method, Lyapunov stability theory and irreducible matrix properties. Furthermore, an event-triggered impulsive control strategy is proposed to control the rumor spreaders and some corresponding control conditions are given. Finally, some numerical simulation results and a practical example are presented to verify the correctness of the theoretical results and reflect the impact of cognitive ability and time delay on rumor propagation.