Epidemiological models have become a very important tool in understanding an epidemic development, mainly because they help researchers in finding good and new strategies in their fight against its spread. Several models have been proposed up to now, some are mathematical others apply models from other areas. The SIR and SEIR among others, mainly focus on the variable response and on epidemiological parameters as the basic reproduction number (R0) and infection rate per unit of time, nevertheless they do not focus on the variable ‘time’. We propose the use of the variable time using the logistic model as it is generally used to describe the growth of animals. This model is important because it allows the estimation of the points of acceleration and deceleration, the point of maximum growth and the asymptotic point of the epidemic. This is only possible when the epidemic curve is stable and has an ‘S’ shape. In this work we use the variable ‘accumulated cases’ of China and Italy and point out the main socioeconomic facts that occurred in each period of the estimated critical points from the logistic growth model.