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

Abstract

A modified ”SIR” epidemic model is proposed taking into account of suitable protein doses thatare applied on the total population as a control to manage a disease outbreak when treatments arenot available. The proteins cause a change in behavior resulting in three susceptible classes. Thestability analysis is studied and the optimal control theory is applied to the system of differentialequations 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.