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As the main methods of the coronavirus disease (COVID-19) transmission are air and physical contact, actions to mitigate and suppress its spread must be developed in order to change population dynamics and provide efficient control strategies. Here, these actions are described as a simple heuristic framework to establish public policies. Two control systems were studied: the first organized in the form of an algorithm stratified into three levels and the second as a minimization problem similar to optimal control strategies, applied to both social distancing and vaccination. The possible effects of these actions are modeled and applied to an extension of the Susceptible - Infected - Removed (SIR) compartmental model. The control system is developed, which is organized in the form of an algorithm stratified into three levels. These levels intend to represent social distancing strategies implemented by sanitary authorities around the globe, representing stronger or weaker grades of isolation intensity according to the ability of the healthcare system to cope with symptomatic individuals. The algorithm control is applied in a simulation, and the results give evidence of the effectiveness of the procedures adopted against the coronavirus. The model dynamics are analyzed and validated with simulations considering parameters obtained from epidemiological data from Brazil and Uruguay and in a more detailed way for three Brazilian states: São Paulo, Minas Gerais and Rio de Janeiro. The model was validated using cumulative data on cases and deaths. For cases of death, the results were satisfactory, while for case data, the response was reasonable, considering the possibility of adding delays or variations in parameters in the model. In addition, the effective reproduction number was proposed for the cities studied in Brazil, the result being relevant because it has a qualitative behavior similar to that published by official centers. This paper also discusses the implementation and optimization of social distancing and vaccination control strategies, considering different parameters and their effects on reducing the number of cases and deaths. Model simulations present promising results for developing strategies to attack COVID-19 dissemination. [ABSTRACT FROM AUTHOR]