Pattern dynamics analysis of higher-order network epidemic-like information propagation model

Abstract

This paper constructs a reaction–diffusion $SI$ (Susceptible-Infected) rumor propagation model based on spatio-temporal factors. This model incorporates higher-order interactions into the reaction terms in order to reflect the complexity of rumor propagation in reality. It has become more realistic and applicable in the complexity of spatiotemporal patterns. In the beginning, we do not consider the diffusion effect and then calculate the equilibrium points of the model with higher-order. The necessary conditions are analyzed for Turing bifurcation to occur. However, the necessary conditions of the Turing bifurcation can only explain the instability of the spatio-temporal propagation of rumors, and cannot accurately predict the spatial distribution pattern of information. Therefore, we have further derived the amplitude equations to predict the evolution of different pattern formations. Finally, we have presented some numerical simulations in different propagation network environments to investigate the influence of various parameters on the distribution density of susceptible populations. Moreover, we use two algorithms to fit the actual data with the model for rumor propagation and conclude that the second method has a better fitting effect.