In the present work, a study is made of the development of epidemics, in particular the one referring to the epidemic transmitted by SAR CoV 2; a model is developed through a system of Differential Equations that simulates this process, the system is simplified, if it makes a qualitative study of the trajectories of the system giving conclusions regarding the hole behavior of the trajectories, thus proving control of the epidemic; a critical case is treated and an example is presented that responds to the conditions of the introduced critical case, graphically proving the conclusions demonstrated analytically.