Model collapse spreads like an epidemic: New SIR framework shows R0 > 1

A new paper on arXiv introduces a groundbreaking epidemiological framework for understanding model collapse, treating synthetic data contamination as a contagious disease spreading across the AI ecosystem. Author Xiangyu Wang proposes a bilayer coupled SIR/SIRS model where data corpora and AI models are two interacting populations, each with susceptible, infected, and recovered compartments linked by cross-layer transmission. Unlike prior analyses that focused on single-chain degradation, this model captures the realistic scenario where models ingest synthetic data from various sources, produce new synthetic text, and contaminate shared corpora—creating a feedback loop that accelerates collapse. The SIRS variant incorporates immunity waning, meaning that even filtered corpora or retrained models remain susceptible to re-contamination.

Experimental validation using GPT-2 on WikiText and Shakespeare (192 contamination chain runs) confirms dose-response degradation and diversity loss consistent with the threshold picture. The basic reproduction number, derived via the Next Generation Matrix, is calculated as R0 = √(β_D β_M / [(γ_D+μ_D)(γ_M+μ_M)]). Calibration from public AI text prevalence data yields R0 > 1 across three scenarios—indicating supercritical, epidemic-like behavior. Sobol sensitivity analysis reveals synthetic-text detection as the highest-leverage parameter, while matched-budget source-diversity experiments (1,088 runs) show that multi-source mixing only modestly attenuates collapse at high contamination fractions. Intervention analysis identifies detection-based filtering and herd immunity as the most effective strategies for containing the spread.