Spatio-temporal pattern formation mechanism of an epidemic-like information propagation model with diffusion behavior

In order to effectively warn against and control the spread of online rumors, it is essential to research the dynamic process of rumor propagation. This paper presents a reaction-diffusion rumor propagation model with a time delay. We analyze the sufficient conditions for the existence of rumor propagation equilibrium points on continuous and complex networks, as well as the conditions for generating Turing bifurcation due to diffusion. Additionally, we derive the amplitude equation of the model to identify the parameter values corresponding to various pattern types. We validate the derivation of the amplitude equation through a series of numerical simulations, providing a robust method for accurately determining the state of rumor propagation. Our study investigates the effect of cross-diffusion coefficients on rumor propagation on the continuous space and finds that these coefficients suppress rumor propagation. Consequently, fostering connections among the public can enhance the dissemination of accurate information and mitigate rumor diffusion. Furthermore, we assess the impact of network node quantity on rumor dissemination on complex networks. Although the number of nodes does not directly influence rumor propagation, a higher node count facilitates a more precise evaluation of rumor propagation status. There is undoubtedly that this is conducive to controlling rumors for managers.