Estimating the state of the Covid-19 epidemic curve in Mayotte during the period without vaccination

We study in this work some statistical methods to estimate the parameters resulting from the use of an age-structured contact mathematical epidemic model in order to analyze the evolution of the epidemic curve of Covid-19 in the French overseas department Mayotte from march 13, 2020 to february 26,2021. Using several statistic methods based on time dependent method, maximum likelihood, mixture method, we fit the probability distribution which underlines the serial interval distribution and we give an adapted version of the generation time distribution from Package R0. The best-fit model of the serial interval was given by a mixture of Weibull distribution. Furthermore this estimation allows to obtain the evolution of the time varying effective reproduction number and hence the temporal transmission rates. Finally based on others known estimates parameters we incorporate the estimated parameters in the model in order to give an approximation of the epidemic curve in Mayotte under the conditions of the model. We also discuss the limit of our study and the conclusion concerned a probable impact of non pharmacological interventions of the Covid-19 in Mayotte such us the re-infection cases and the introduction of the variants which probably affect the estimates.