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The emergence of different virus variants, the rapidly changing epidemic, and demands for economic recovery all require continual adjustment and optimization of COVID-19 intervention policies. For the purpose, it is both important and necessary to evaluate the effectiveness of different policies already in-place, which is the basis for optimization. Although some scholars have used epidemiological models, such as susceptible-exposed-infected-removed (SEIR), to perform evaluation, they might be inaccurate because those models often ignore the time-varying nature of transmission rate. This study proposes a new scheme to evaluate the efficiency of dynamic COVID-19 interventions using a new model named as iLSEIR-DRAM. First, we improved the traditional LSEIR model by adopting a five-parameter logistic function $\beta \left(t\right)$ to depict the key parameter of transmission rate. Then, we estimated the parameters by using an adaptive Markov Chain Monte Carlo (MCMC) algorithm, which combines delayed rejection and adaptive metropolis samplers (DRAM). Finally, we developed a new quantitative indicator to evaluate the efficiency of COVID-19 interventions, which is based on parameters in $\beta \left(t\right)$ and considers both the decreasing degree of the transmission rate and the emerging time of the epidemic inflection point. This scheme was applied to seven cities in Guangdong Province. We found that the iLSEIR-DRAM model can retrace the COVID-19 transmission quite well, with the simulation accuracy being over 95% in all cities. The proposed indicator succeeds in evaluating the historical intervention efficiency and makes the efficiency comparable among different cities. The comparison results showed that the intervention policies implemented in Guangzhou is the most efficient, which is consistent with public awareness. The proposed scheme for efficiency evaluation in this study is easy to implement and may promote precise prevention and control of the COVID-19 epidemic. Full article