Early warning signals in rumor models

We study the emission and control of a rumor using the modified Maki-Thomson model. A key challenge in social networks is distinguishing between natural increases in transmissibility and artificial injections of rumor spreaders, such as through broadcast events or astroturfing. Using stochastic simulations, we compare two scenarios: one with organic growth in transmissibility, and another with externally injected spreaders. Although both lead to high autocorrelation, only the organic growth produces oscillatory patterns in autocorrelation at multiple lags, an effect we can analytically explain using the N-intertwined mean-field (NIMFA) approximation. This distinction offers a practical tool to identify the origin of rumor virality and also infer its transmissibility. Our approach is validated analytically and tested on real-world data from Twitter during the announcement of the Higgs boson discovery. In addition to detection, we also explore control strategies. We show that the average lifetime of a rumor can be manipulated through targeted interventions: placing spreaders at specific locations in the network. Depending on their placement, these interventions can either extend or shorten the lifespan of the rumor.