DYNAMIC ANALYSIS OF A RUMOR PROPAGATION MODEL

Rumor propagation rapidly and can cause significant damage. Based on the premise of a rumor management mechanism, this study analyzes the propagation rules among latent disseminators, disseminators, and non- disseminators. We have crafted a rumor propagation model and have established the presence of an equilibrium state within it. Additionally, we have analyzed the local and global stability of this equilibrium, as well as determined the model's propagation threshold. By determining the equilibrium point of the model, we examine the link between this issue and the crisis's progression pattern, and derive the threshold R0. The propagation-free equilibrium is stable within a certain range when R0 < 1, and propagation exhibits a downward trend until it ultimately subsides. Subsequently, the factors affecting the threshold R0 are investigated through numerical experiments. Finally, the influence of these factors on the development trend of rumor is analyzed in detail. This research can help authorities understand the principles of propagation and offer guidance.