Applied Mathematics & Information Sciences

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In this paper, we formulate an optimal control problem for an SIR epidemic model with saturated incidence and saturated treatment. Two main efforts, namely treatment and vaccination are considered to limit the disease transmission. The impacts of vaccination and treatment on the disease transmission are discussed through the basic reproduction number. Then to achieve control of the disease, a control problem is formulated and the existence of the control is shown. Two control functions are used, one for vaccinating the susceptible and the other for treatment efforts for infectious individuals. Appropriate optimal control methods are used to characterize the optimal levels of the two controls. The effectiveness of the proposed control solution is shown by comparing the behavior of controlled and uncontrolled systems. Numerical results show the impacts of two controls in decreasing both susceptible and infectious members of the population.

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