Fast-variable reduction to complex contagion unifies epidemic models
Abstract
Across biological and social complex systems, models of epidemics or contagions incorporate complexity through network correlations, adaptive behavior, higher-order interactions, or co-circulating strains. Tracking these mechanisms lead to high-dimensional mathematical systems that resist analytical treatment. We show that a broad class of models admits a systematic reduction via fast-variable elimination. The central insight is that complexity can be captured by fast variables equilibrating much faster than the epidemic, leading to ``emergent complex contagion'' where the force of infection depends on prevalence. The epidemic transition follows a universal equation and is continuous or discontinuous whether the force of infection decays or intensifies with prevalence. Our results reveal diverse epidemic models share a common skeleton such that mechanisms that share a characteristic form can be macroscopically indistinguishable.
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BibTeX
@misc{hebertdufresne2026fastvariable,
title = {{Fast-variable reduction to complex contagion unifies epidemic models}},
author = {Laurent Hébert-Dufresne and Péter L. Simon and István Z. Kiss},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.05467},
eprint = {2610.05467},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.05467},
}
RIS
TY - UNPB
TI - Fast-variable reduction to complex contagion unifies epidemic models
AU - Laurent Hébert-Dufresne
AU - Péter L. Simon
AU - István Z. Kiss
PY - 2026
DA - 2026/10/04
PB - arXiv
DO - 10.48550/arxiv.2610.05467
UR - https://arxiv.org/abs/2610.05467
AB - Across biological and social complex systems, models of epidemics or contagions incorporate complexity through network correlations, adaptive behavior, higher-order interactions, or co-circulating strains. Tracking these mechanisms lead to high-dimensional mathematical systems that resist analytical treatment. We show that a broad class of models admits a systematic reduction via fast-variable elimination. The central insight is that complexity can be captured by fast variables equilibrating much faster than the epidemic, leading to ``emergent complex contagion'' where the force of infection depends on prevalence. The epidemic transition follows a universal equation and is continuous or discontinuous whether the force of infection decays or intensifies with prevalence. Our results reveal diverse epidemic models share a common skeleton such that mechanisms that share a characteristic form can be macroscopically indistinguishable.
ER -