# Narrative Economics - SIR Model

Interactive visualization of how economic narratives spread like epidemics using the SIR model

> Canonical page: https://elysiatools.com/en/visualizations/narrative-economics

- **Category:** Math

## Overview

Interactive visualization of how economic narratives spread like epidemics using the SIR (Susceptible-Infected-Recovered) model from epidemiology, pioneered by Nobel laureate Robert Shiller. Features the fundamental differential equations: dS/dt = -c·S·I (narrative spreads through contagion), dI/dt = c·S·I - r·I (active spreaders), dR/dt = r·I (people lose interest), where c is contagion rate (how quickly narrative spreads), r is recovery rate (how quickly people stop spreading), and basic reproduction number R₀ = c/r determines epidemic potential (R₀ > 1: narrative grows, R₀ < 1: narrative dies out). Five interactive modules: (1) SIR Simulation with real-time animated curves showing S(t) declining, I(t) bell curve, R(t) rising, adjustable parameters c (0-1), r (0-1), population N (100-10000), initial infected I₀, optional SIRS model for narrative recurrence, and play/pause/reset controls; (2) Phase Plane Analysis with 2D S vs I trajectory visualization, streamlines showing vector field, nullclines (dI/dt=0 vertical line at S=N·r/c, dS/dt=0 horizontal axes), click-to-set initial conditions, multiple trajectory comparison, and current state display; (3) Parameter Exploration with four preset scenarios (Viral Spread: c=0.8, r=0.2, R₀=4.0; Quick Fade: c=0.1, r=0.5, R₀=0.2; Sustained: c=0.3, r=0.3, R₀=1.0; Recurrent Narrative: SIRS with periodic resurgence), side-by-side scenario comparison chart, and one-click scenario application; (4) Real Historical Cases featuring Laffer Curve narrative (1970s-80s supply-side economics), Great Recession narrative (2008-2009 Great Depression comparison), Bitcoin "Get Rich Quick" narrative (2017 crypto boom), each with peak timing, duration estimates, and stylized intensity curves; (5) Educational Content covering mathematical derivation of SIR equations, R₀ interpretation and economic significance, contagion parameter factors (emotional resonance, simplicity, social media amplification, authority endorsements), recovery parameter factors (attention span, competing narratives, counter-evidence, narrative fatigue), social media impact on c (network effects, algorithmic amplification, echo chambers), and policy applications (predicting market bubbles, designing communications, countering harmful narratives). Uses Runge-Kutta 4th order numerical integration for accurate solution of differential equations. Visualizes narrative bell curve characteristic, epidemic threshold behavior, and recurrent patterns. Color coding: blue (Susceptible), red (Infected), green (Recovered). Real-time R₀ calculation with meaning display (High/Low/Critical). Responsive design with touch support for mobile. Multi-language support (zh, en, es, fr, de, ru, pt).

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