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abstract: 'Ever since the outbreak of the COVID-19 epidemic, various public health control strategies have been proposed and tested against SARS-CoV-2. In this paper, we study three specific COVID-19 epidemic control models: the susceptible, exposed, infectious, recovered (SEIR) model with vaccination control, the SEIR model with shield immunity control, and the susceptible, un-quarantined infected, quarantined infected, confirmed infected (SUQC) model with quarantine control. We express the control requirement in *metric temporal logic* (MTL) formulas and develop methods for synthesizing control inputs based on three specific COVID-19 epidemic models with MTL specifications. To the best of our knowledge, this is the first paper to provide automatically-synthesized and fine-tuned control synthesis for the COVID-19 epidemic models with formal specifications. We provide simulation results in three different case studies: vaccination control for the COVID-19 epidemic with model parameters estimated from data in Lombardy, Italy; shield immunity control for the COVID-19 epidemic with model parameters estimated from data in Lombardy, Italy; and quarantine control for the COVID-19 epidemic with model parameters estimated from data in Wuhan, China. The results show that the proposed synthesis approach can generate control inputs within a relatively short time (within 5 seconds) such that the time-varying numbers of 