Control strategies and virality detection using early warning signals in rumor models

TL;DR

The paper tackles distinguishing endogenous versus externally driven virality in rumor spreading using a modified Maki–Thompson model with forgetting, analyzed via NIMFA and stochastic simulations. It introduces early warning signals and multi-lag autocorrelation to detect critical slowing down and oscillatory dynamics in a metastable regime, enabling inference of transmissibility changes. It also demonstrates practical control strategies by strategically placing spreaders to extend or shorten rumor lifetime, and validates the approach on Higgs boson–announcement Twitter data to show nowcasting of internal transmission shifts. The work contributes to disinformation detection and mitigation by providing a computationally light, signal-driven framework grounded in non-equilibrium dynamics.

Abstract

We study the dynamics and intervention strategies of a rumor using the modified Maki-Thompson 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.

Figures (14)

• Figure 1: Experiment setting with a simplified network representation (above) and average lifetime of finite realizations of the interventions (below). A shows the intervention of adding an external spreader far away from the initial one, increasing the lifetime of the rumor. B shows the intervention of adding an external spreader close to the initial one, resulting of a decrease in the lifetime. The $s$ indicates the initial spreader (seed). The plots below show the average lifetime as a function of the spreading rate with the approximation for the intervention (continuous lines) and without (discontinuous lines) for both cases. The parameters are: $\alpha = 0.5, \delta = 1$ and the network is of size $N = 1000$ and $\langle k\rangle = 10$.
• Figure 2: The circles indicate the average lifetime of finite realizations of the process starting with a single spreader. The triangles indicate the average time of appearance of the first stifler in the system the squares indicate the average time of appearance of the second spreader. The dashed lines indicate the approximation found for both cases. The parameters are: $\alpha = 0.5, \delta = 1$ and the network is of size $N = 1000$ and $\langle k\rangle = 10$.
• Figure 3: The autocorrelation as a function of the spreading rate ($\lambda$) at multiple lags of the density of spreaders starting from a single spreader. The red dashed line indicates the average lifetime ($\tau$) of finite realizations. The autocorrelation is computed using the quasi-stationary method. The parameters used are $\delta =0.89, \alpha = 0.5$ for a network of size $N = 1000$ and $\langle k\rangle=10$.
• Figure 4: Representation of the two scenarios: (1) sudden transmissibility rate increase ($\lambda$) and (2) external impulse with fixed spreading rate. For the scenario 2 we simulate: in (a) a sudden density pulse of permanent spreaders located at a random position in the network; (b) a pulse of permanent spreaders added next to an spreader (localized); (c) a pulse of spreaders that become common population (transient) at a random position; and (d) a fixed rate with a pulse of converted as common population added next to an spreader. At the bottom there is the analysis of the mutual information (MI) at random nodes and the autocorrelation (AC) of the spreaders density. Simulations were performed on a random regular network of degree 10, with averaged values from 1000 realizations and analyzed with a rolling window of 50 process steps. The parameters are: $\alpha = 0.5, \delta = 0.89$ and the network is of size $N = 1000$ and $\langle k\rangle = 10$, the external perturbation is of 50 new spreaders. The information regarding simulation details can be found in the Appendix \ref{['methods']}.
• Figure 5: At the left, the autocorrelation of spreaders density as a function of lag after the perturbation for the different scenarios: the transmissibility increase (dynamic $\lambda)$ and the external impulse with permanent and transient spreaders. At the right, the new spreaders density is analyzed for the same cases. The new spreaders are counted as the new infected nodes during each time step.