The study of epidemiological models are important because they help researchers to understand and propose possible strategies to combat any epidemic virus. Most of the research in those models, however, focuses on the response variable, modeling how it varies as a function of epidemiological parameters. In this paper, on the other hand, we focus on the explanatory variable ”time,” examining the critical points of the logistic model curve. These are: the maximum acceleration point(map), inflection point(ip), maximum deceleration point(mdp), and asymptotic deceleration point(adp). We first estimated a time series of the cases of people infected by COVID 19 as a function of time, and then used the cumulative estimates of the time series to fit a reparameterization of the logistic model. Data from China and Italy were used as an example, reporting the economic and political factors within each interval between the estimated critical points. The estimates of each critical point for China and Italy were respectively (map:34.93-50.92, ip:41.68-65.53;mdp:48.43-80.14;adp:57-94). Thismethodology adds to the literature and shows researchers how the social, political, economic, and sanitary factors that were adopted in each of the countries influenced the difference of the intervals between the critical points in each country.