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In this paper, with nonlinear inhibitory effect and saturated treatment rate, an SEIR epidemic model is proposed. The basic reproduction number R0, is calculated when determining the threshold value for the disease and the dynamics of the model. The criteria for the existence of all the points of equilibrium are established and we also found that the conditions depend on them. The stability of equilibrium is discussed in terms of local and global. All attempted were made to present the numerical simulations for the model we suggested. The theoretical findings are clearly predicted to be supported and evaluated.

Mathematical study of SEIR model with functional rates of incidence and treatment