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Here we introduce the Epi-LLM framework: a novel integration of agent-based modelling, real-life epigames, and large language models (LLMs) in which a synthetic society of agents reasons and adapts dynamically over an outbreak contact network. Comparing synthetic agent behaviour against a no-intervention SEIR baseline and human participant data from the AUIB epigame study, we find that LLM agents across four different architectures reduced peak active infections, with quarantine compliance peaking at 58-65% on day six of the 15-day simulation. A binomial generalised linear model showed that perceived health severity was the strongest predictor of quarantine behaviour ($\\beta = 0.33, p = 0.002$), yielding a pseudo-$R^2$ of 0.055, comparable to the 0.072 observed in the human trial. 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A binomial generalised linear model showed that perceived health severity was the strongest predictor of quarantine behaviour ($\\beta = 0.33, p = 0.002$), yielding a pseudo-$R^2$ of 0.055, comparable to the 0.072 observed in the human trial. 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