Optimal Control of an ”SIR” Epidemic Model in a Chemostat Using Some Suitable Protein Doses

A modified ”SIR” epidemic model is proposed taking into account of suitable protein doses that are applied on the total population as a control to manage a disease outbreak when treatments are not available. The proteins cause a change in behavior resulting in three susceptible classes. The stability analysis is studied and the optimal control theory is applied to the system of differential equations to achieve the goal of minimizing the infected population (while minimizing the cost). Some numerical simulations are given in order to illustrate the obtained results.