OBJECTIVE Assuming the availability of a limited amount of effective COVID-19 rapid tests, the effects of various vaccination strategies on SARS-CoV-2 virus transmission are compared for different vaccination scenarios characterized by distinct limitations associated with vaccine supply and administration. METHODS The vaccination strategies are defined by solving optimal control problems of a compartmental epidemic model in which the daily vaccination rate and the daily testing rate for the identification and isolation of asymptomatic subjects are the control variables. Different kinds of algebraic constraints are considered, representing different vaccination scenarios in which the total amount of vaccines available during the time period under consideration is limited or the number of daily available vaccines is limited. These optimal control problems are numerically solved by means of a direct transcription technique, which allows both equality and inequality constraints to be straightforwardly included in the formulation of the optimal control problems. RESULTS Several numerical experiments are conducted, in which the objective functional to be minimized is a combination of the number of symptomatic and asymptomatic infectious subjects with the cost of vaccination of susceptible subjects and testing of asymptomatic infectious subjects. The results confirm the hypothesis that the implementation of early control measures significantly reduces the number of symptomatic infected subjects, which is a key aspect for the resilience of the healthcare system. The sensitivity analysis of the solutions to the weighting parameters of the objective functional reveals that it is possible to obtain a vaccination strategy that allows vaccination supplies to be saved while keeping the same number of symptomatic infected subjects. Furthermore, it indicates that if the vaccination plan is not supported by a sufficient rate of testing, the number of symptomatic infected subjects could increase. Finally, the sensitivity analysis shows that a significant reduction in the efficacy of the vaccines could also lead to a relevant increase in the number of symptomatic infected subjects. CONCLUSIONS The numerical experiments show that the proposed approach, which is based on optimal control of compartmental epidemic models, provides healthcare systems with a suitable method for scheduling vaccination plans and testing policies to control the spread of the SARS-CoV-2 virus.