Mean-field propagation model

This simulator uses a mean-field (aggregated) branching process to model viral content propagation across a large social network. Rather than tracking individual accounts, it carries aggregate state for active shares, cumulative reach, and manipulation exposure, evolving them in discrete one-minute steps. Growth follows active shares times the effective reproduction number times the susceptible fraction, plus seed ingress. The baseline scenario is unrestricted propagation; the policy scenario applies friction mechanisms designed to suppress coordination attacks and shrink the political manipulation surface.

Reproduction number and threshold

The basic reproduction number is the product of fan-out, reshare probability, and amplification, R0 = avgDegree times shareProb times amplification. Policy levers act as multipliers that pull it down to an effective R_eff. The epidemic threshold theorem decides the outcome: a cascade is supercritical (self-sustaining, growing) when R_eff is above 1 and subcritical (fading) when it is at or below 1. Above threshold a finite fraction of the audience is eventually reached, the final-size fraction one minus one over R_eff.

Policy mechanics

Seven levers modulate the dynamics. A 10-hour cooldown restricts accounts to about 2.4 posts per day; a 10-hour coolup delays visibility and damps ignition; a 1-hour daily window further constrains election-period posting; forward caps halve effective fan-out; question-gating and prebunking lower both reshare probability and conversion; identity tiers impose stricter friction on new or low-trust accounts; per-thread slow mode applies temporal smoothing. Each is encoded as an independent multiplier on rate, visibility, fan-out, or conversion, and they compose to reduce R_eff, delay cascades, and diminish manipulation impact.

Political manipulation impact

The PMI index accumulates, at each step, new exposures times the effective per-exposure conversion probability. Conversion decays with content age through an attention half-life, so delayed content lands with diminished potency, and question-gating applies an extra skepticism reduction. The model reports absolute PMI for both scenarios and the percentage reduction under policy, capturing not just lower reach but the qualitative degradation of manipulation potency due to delay and friction.

What it is not

The mean-field approximation trades agent-level fidelity for tractability. It assumes well-mixed contact, simple contagion, static multiplier policies, and a proxy conversion count, none of which hold exactly in real graphs with hubs, complex contagion, adaptive adversaries, and heterogeneous persuasion. Parameters are tuned for pedagogical visibility of policy effects, not quantitative forecasting. Results illustrate comparative trends and mechanism interactions rather than precise predictions.

Implementation

Calibration

Assumptions

Model changelog