AbstractIn order to anticipate a future trends in the development of the novel coronavirus COVID-19 epidemic started early at march 13, in the french overseas department Mayotte, we consider in this paper a modified deterministic and stochastic epidemic model. The model divides the total population into several possible states or compartment: susceptible (S), exposed (E) infected and being under an incubation period, infected (I) being infectious, simple or mild removed RM, severe removed (including hospitalized) RS and death cases (D). The adding of the two new compartment RM and RS are driven by data which together replace the original R compartment in the classical SEIR model.We first fit the constant transmission rate parameter to the epidemic data in Mayotte during an early exponential growth phase using an algorithm with a package of the software R and based on a Maximum Likewood estimator. This allows us to predict the epidemic without any control in order to understand how the control measure and public policies designed are having the desired impact of controlling the epidemic. To do this, we introduce a temporally varying decreasing transmission rate parameter with a control or quarantine parameter q. Then we pointed out some values of q to maintain control which is critical in Mayotte given the fragility of its health infrastructure and the significant fraction of the population without access to water.