ABSTRACT
We study in this article some statistical methods to fit some epidemiological parameters. We first consider a fit of the probability distribution which underlines the serial interval distribution of the COVID-19 on a given set of data collected on the viral shedding in patients with laboratory-confirmed. The best-fit model of the non negative serial interval distribution is given by a mixture of two Gamma distributions with different shapes and rates. Thus, we propose a modified version of the generation time function of the package R0. Second, we estimate the time-varying reproduction number in Mayotte. Using a justified mathematical learning model, we estimate the transmission parameters range values during the outbreak together with a sensitivity analysis. Finally, using some regression and forecasting methods, we give some learning models of the hospitalized, intensive care, and death cases over a given period. We end with a discussion and the limit of this study together with some forthcoming theoretical developments.