Estimating COVID-19 vaccine protection rates via dynamic epidemiological models—a study of 10 countries

The real-world performance of vaccines against COVID-19 infections is critically important to counter the pandemics. We propose a varying coefficient stochastic epidemic model to estimate the vaccine protection rates based on the publicly available epidemiological and vaccination data. To tackle the challenges posed by the unobserved state variables, we develop a multistep decentralized estimation procedure that uses different data segments to estimate different parameters. A B-spline structure is used to approximate the underlying infection rates and to facilitate model simulation in obtaining an objective function between the imputed and the simulation-based estimates of the latent state variables, leading to simulation-based estimation of the diagnosis rate using data in the prevaccine period and the vaccine effect parameters using data in the postvaccine periods. The time-varying infection, recovery and death rates are estimated by kernel regressions. We apply the proposed method to analyze the data in ten countries which collectively used eight vaccines. The analysis reveals that the average protection rate of the full vaccination was at least 22% higher than that of the partial vaccination and was largely above the WHO recognized level of 50% before November 20, 2021, including the Delta variant dominated period. The protection rates for the booster vaccine in the Omicron period were also provided.