Our goal in this paper is to adapt to the context of the Greater Abidjan Region (Côte d'Ivoire) an existing model reflecting the evolution of the COVID-19 epidemic in Wuhan (China). This model is a deterministic compartmental model which is translated by a system of ordinary differential equations. We are reinvesting this model to obtain the parameters of the epidemic in the great Abidjan. We study some mathematical aspects of this deterministic model.Using data from the evolution of the COVID-19 epidemic in Abidjan, we obtain constants corresponding to the Greater Abidjan Region epidemic. We are performing numerical simulations using these constants to predict the behavior of the epidemic in the Greater Abidjan Region.The initial model does not take into account certain disturbances and sudden shocks which could disturb its behavior. In the Greater Abidjan Region, some continuous or sudden events disrupt the behavior of the epidemic. To stick to the realities of the Greater Abidjan Region, we introduce a white noise and jumps that correspond to the different disturbances that can occur. We obtain a stochastic model of COIVD-19 with jumps. We prove that our new model with jumps has a positive global solution. In certain conditions, this solution oscillates in the set of the disease-free equilibrium of the deterministic model. We perform numerical simulations which corroborate our theoretical results.