A Dynamic Competition and Predation Model for Rumor and Rumor-Refutation

Controlling rumors is related to the interplay between the rumor and rumor refutation, which compete to attract the unaware. And rumor refutation preys on the rumors, and try to eliminate rumors. Therefore, there is both a predatory and competitive relationship between the rumors and the rumor refutations. This paper presents a model based on biomathematics theory to describe the interplay between rumors and rumor refutations. The theoretical analysis of the differential equations elucidated three dynamic cases: rumor extinction; rumor refutation extinction; and rumor and rumor refutation coexistence. The subsequent analysis of the equilibrium stability in the three cases revealed both equilibrium stability and model instability. The haze rumor and the official haze refutation data were then crawled from Sina microblog, the rumor propagation process analyzed, an integral method employed for the model parameter estimation, and the proposed model used to estimate and forecast the haze rumor and rumor-refutation evolutions. The findings suggested that rumors and rumor refutations coexist, which was consistent with the theoretical analysis of coexistence. Based on this case and to more deeply analyze the effect of an authority's credibility and the public's cognition, the proposed model was used to suggest several scenarios, and policy suggestions given to assist authorities better manage rumors in emergency events.