The mutual cooperation and coordinated response of local governments, social organizations and the public in public health emergencies is an inevitable choice for timely and efficient emergency management. By taking the COVID-19 epidemic as the background, we consider the interaction and game relationship between multiple subjects in the emergency response process, and based on the assumption of bounded rationality, constructs a dynamic game model of the evolution of the three parties of the local government, social organizations and the public. Then, by using evolutionary game theory and Lyapunov discriminant method to analyze the equilibrium point and asymptotic stability of the tripartite evolution model, we obtain the evolutionary stable strategy of the tripartite subject under different conditions. Finally, the game behavior of the tripartite emergency response in different stages of public health emergencies is simulated and analyzed, and the influence of local government subsidy policies, reward and punishment measures, and social organization costs on the strategic choices of all parties in the game are discussed. The research results show that: (1) in different stages of emergency response to public health emergencies, the decision-making choices of each subject evolve dynamically; (2) local government subsidy policies, reward and punishment measures, and social organization costs have a significant effect on the subject's emergency response behavior; (3) the initial participation willingness of each subject has a significant impact on the emergency response to public health emergencies.
