AI agents are increasingly deployed as quasi-autonomous systems for specialized tasks, yet their potential as computational models of decision-making remains underexplored. We develop a generative AI agent to study repetitive policy decisions during an epidemic, embedding the agent, prompted to act as a city mayor, within a simulated SEIR environment. Each week, the agent receives updated epidemiological information, evaluates the evolving situation, and sets business restriction levels. The agent is equipped with a dynamic memory that weights past events by recency and is evaluated in both single- and ensemble-agent settings across environments of varying complexity. Across scenarios, the agent exhibits human-like reactive behavior, tightening restrictions in response to rising cases and relaxing them as risk declines. Crucially, providing the agent with brief systems-level knowledge of epidemic dynamics, highlighting feedbacks between disease spread and behavioral responses, substantially improves decision quality and stability. The results illustrate how theory-informed prompting can shape emergent policy behavior in AI agents. These findings demonstrate that generative AI agents, when situated in structured environments and guided by minimal domain theory, can serve as powerful computational models for studying decision-making and policy design in complex social systems.