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Seroprevalence of SARS-CoV-2 antibodies in South Korea

In $2020$, Korea Disease Control and Prevention Agency reported three rounds of surveys on seroprevalence of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) antibodies in South Korea. We analyze the seroprevalence surveys using a Bayesian method with an informative prior distribution on the seroprevalence parameter, and the sensitivity and specificity of the diagnostic test. We construct the informative prior using the posterior distribution obtained from the clinical evaluation data based on the plaque reduction neutralization test. The constraint of the seroprevalence parameter induced from the known confirmed coronavirus 2019 cases can be imposed naturally in the proposed Bayesian model. We also prove that the confidence interval of the seroprevalence parameter based on the Rao's test can be the empty set, while the Bayesian method renders a reasonable interval estimator. As of the $30$th of October $2020$, the $95\%$ credible interval of the estimated SARS-CoV-2 positive population does not exceed $307,448$, approximately $0.6\%$ of the Korean population.