Global dynamics of delayed discrete-time SEIR negative information propagation model with multi-platform and cross-transmission mechanism

Taking into account the phenomenon of cross-platform propagation of network information and multi-platform network environments, this paper constructs two discrete-time negative information propagation models with time delays. For the single platform model, we first prove that the information-free equilibrium (IFE) is locally asymptotically stable (LA-stable) and globally asymptotically stable (GA-stable) when ${ℛ}_0<1$. Then, by using the method of Lyapunov function, it is obtained that when ${ℛ}_0>1$, the information-spreading equilibrium (ISE) is GA-stable. For the multi-platform model, it is found that its dynamic behaviors are completely determined by the propagation threshold ${\hat{\Re }}_0$. To be specific, the IFE of the multi-platform model is GA-stable when ${\hat{\Re }}_0<1$. With respect to ${\hat{\Re }}_0>1$, it is proved that the ISE is GA-stable by using graph theory approach. The numerical experiments verify the accuracy of the conclusions. In the end, a real case is selected to illustrate the applicability of the model.