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The problem of repeated epidemic fluctuations in the normalized prevention and control stage is revealed by data from January 20, 2020, to January 30, 2023. In order to improve the collaborative response of the public and government departments to public health emergencies and avoid repeated fluctuations of the epidemic, a tripartite evolutionary game model of the public, local government, and central government departments is constructed, focusing on the evolutionary paths and evolutionary stabilization strategies of the three subjects, and the influence of each element on the evolutionary results is simulated by numerical simulation in Matlab, and based on the inadequacy of the static reward and punishment mechanism, a dynamic Based on the shortcomings of static reward and punishment mechanism, dynamic reward and punishment mechanism is introduced to control the stability of the evolving system. The study shows that (1) with the increase of the initial willingness of the three parties, the rate of the public choosing the discretionary flow strategy slows down, and the collaborative prevention and control process can be accelerated. (2) The reward and punishment mechanism of central government departments has a positive incentive effect on the local government's strict prevention and control and the public's conscious isolation. Appropriately increasing rewards, formulating reasonable subsidy strategies, and increasing penalties for violations are conducive to the overall optimization of the system, and the punishment mechanism is most sensitive to the regulation of the public's discretionary mobility behavior. (3) Government departments' prevention and control costs can influence their enthusiasm for strict prevention and control and real-time supervision. Reducing the human resources cost, time cost, and financial cost of prevention and control is conducive to government departments performing their duties more responsibly. (4) The static punishment mechanism fails to make timely adjustments according to the strategy choice of each actor. It cannot control the stability of the evolving system. In contrast, the dynamic punishment mechanism considers the punishment parameters to link the casual isolation rate with the lenient prevention and control rate, which can effectively control the system's fluctuating instability and is the system's stability control strategy. Finally, combining theoretical and simulation analysis, management suggestions are made for controlling repeated fluctuations of the epidemic in practice, and the research limitations of this paper are explained., (© 2024. The Author(s).)