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In the present work, we consider a mathematical model of an SIR epidemic model with saturated incidence rate and saturated treatment function. We use an optimal vaccination strategies to minimize the susceptible and infected individuals and to maximize the number of recovered individuals. We work in the nonlinear optimal control framework. Some results concerning the existence and the characterization of the optimal control will be given. Numerical simulations are also presented.
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Laarabi et al. (2013) studied this question.
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