A mathematical model has been created with the Systems Dynamics methodology. It is based on a SIR model, with the addition of auxiliary and state variables that represent hospital capacity, contacts, contacts with infected, deaths, giving, as a result, a model of four stock variables. Similarly, using piecewise functions, it was possible to model the “quarantines” or lockdowns, and the effectiveness of reduction in the contacts, Results show the decrease in infected people due to the quarantines. The model was simulated for a population of 100,000. The simulations show trends of infections that could occur in three different scenarios: A) one extended lockdown (60 days), B) two medium lockdowns of 30 days, with a 30-day smart lockdown space, and C) an initial 40- day lockdown and then a 30-day smart lockdown. All the lockdowns start on day 25 after the first reported infection. The model presents a compact structure of broad understanding and successful capture of a COVID-19 outbreak and therefore provides an overview to improve knowledge of outbreak trends and quarantine effectiveness in reducing infection.