M1 Sub-critical diffusion, viral cascade or saturation

Topic

This pathway can manifest in three distinct modes depending on how far an idea, rumor, or behavior travels as it spreads through the social network: a sub-critical mode, where the spread dies out before reaching a significant fraction of the network; a viral cascade mode, where the spread accelerates and reaches an increasing fraction of the network; and a saturation mode, where the spread slows down because it has already reached the maximum fraction of the network willing to adopt it. The variable triggering the transition between these three modes is the social reproduction number—the same metric used to diagnose this pathway—which measures how many new adoptions each adopter generates on average, in direct analogy to the basic reproduction number of an epidemic.

When the social reproduction number remains below a reference threshold, the diffusion is sub-critical and dies out on its own without requiring external intervention; when it crosses that threshold in a sustained manner, the diffusion enters viral cascade mode—a sustained crossing that the pathway’s diagnostic already identified as the direct trigger for this mode; and when the fraction of the network willing to adopt is exhausted, the diffusion enters saturation mode, corresponding to the "time to saturation" metric already measured in that diagnostic.

Viral cascade mode is not, in itself, a viral misinformation cascade: a true idea or a harmless behavior can also achieve a social reproduction number above the threshold and spread in viral cascade mode without constituting an anomaly. What turns this mode into the specific anomaly in question is the rate of debunking and correction falling far behind that speed of spread: the mode simply describes how far the diffusion reaches, whereas the anomaly describes what happens when, in addition, no one manages to correct it in time. A channel operating in a viral cascade mode with an equally high correction rate can sustain propagation without slipping into a cascade of viral misinformation; it is the absence of that correction—not the speed of propagation itself—that distinguishes a stable mode from an anomaly.

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