Emergence of unquenchable rumors with extended SIR epidemic model

With the advent of the internet era, certain inaccurate news items, namely rumors, have become increasingly difficult to manage and even hard to eradicate. In this paper, considering the characteristics of information communication in current time, we extend the classic SIR infectious diseases model from a neighbor communication mechanism to a non-neighbor communication mechanism. We find that under the new communication mechanism, if there is a situation where the credibility of a rumor is greater than the credibility of the truth, and the intensity parameters for governing the rumor have also been determined, then once the number of people potentially spreading the rumor exceeds a certain threshold, the rumor is no longer controllable, i.e., there will be persistent rumors that will never disappear. This is a new emergence mechanism in the era of Internet. In this paper, we study this nonlinear mechanism both theoretically and numerically.