In this paper, it is shown that the Moyal distribution is an excelent tool to study the SARS-Cov-II (Covid-19) epidemiological associated curves and its propagation. The Moyal parameters give all the information to describe the form and the impact of the illness outbreak in the different affected countries and its global impact. We checked that the Moyal distribution can accurately fit the daily report of {it{new confirmed cases of infected people}} (NCC) per country, in that places where the contagion is reaching their final phase, describing the beginning, the most intense phase and the descend of the contagion, simultaneously . In order to achieve the purpose of this work, it is important to work with a complete and well compilated set of the data to be used to fit the curves. Data from European countries like France, Spain, Italy Belgium, Sweden, United Kingdom, Denmark and others like USA and China, have been used. Also, the correlation between the parameters of the Moyal distribution fitting and the general public health measures imposed in each country, have been discussed. A relation between those policies and the features of the Moyal distribution, in terms of their parameters and critical points, is shown; from that, it can be seen that the knowledge of the time evolution of the epidemiological curve, their critical points, superposition properties and rates of the rising and the ending, could help to find a way to estimate the efficiency of social distancing measures, imposed in each country, and anticipate the different phases of the pandemic.
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