In this paper, the interaction strategies and the evolutionary game analysis of the actions taken by the government and the public in the early days of the epidemic are incorporated into the natural transmission mechanism model of the epidemic, and then the transmission frequency equations of COVID-19 epidemic is established. According to the cumulative confirmed cases of COVID-19 in the UK and China, the upper limit of the spread of COVID-19 in different evolutionary scenarios is set. Using SPSS to perform logistic curve fitting, the frequency fitting equations of cumulative confirmed cases under different evolution scenarios are obtained respectively. The analysis result shows that the emergency response strategy adopted by the government in the early days of the epidemic can effectively control the spread of the epidemic. Combined with the transmission frequency equation of COVID-19 epidemic, measures taken by the government are analyzed. The influence of each measure on the frequency variable is judged and then the influence on the spread of the epidemic is obtained. Finally, based on the above analysis, the government is advised to adhere to the principles of scientific, initiative and flexibility when facing major epidemics.