Abstract: The COVID-19 that broke out at the end of 2019 is highly contagious, the world is caught in panic of the epidemic, and the cumulative number of confirmed cases is still on the rise. Since the outbreak of covid-19 in China, the government has taken decisive measures to control the epidemic. In the process of isolation prevention and control, there is a game relationship between government departments and the public. It is assumed that both the government and the public are bounded rational groups and the evolutionary game model is used, a game matrix is constructed for government departments and the public under static and three dynamic reward and punishment mechanisms,analyzing the impact of prevention and control costs, the upper limit of reward and the upper limit of punishment on the evolutionary and stable strategy of the game system.Finally, a simulation analysis is performed.The results show that:there is no evolutionary stable strategy under static reward and punishment mechanisms,the use of dynamic reward and punishment mechanisms can effectively make up for the shortcomings of static reward and punishment mechanisms,achieving the evolution and stability of government departments’ active prevention and control and the public’s voluntary isolation strategy;dynamic reward and static punishment is better than other mechanisms; The probability of voluntary segregation by the public is negatively correlated with the cost of prevention and control and the upper limit of reward,positively correlated with the upper limit of punishment.

Key words: evolutionary game; major epidemic prevention and control; the mechanism of dynamic reward and punishment; evolutionary stable strategy