Optimal control of an inflammatory immune response model

A reduced model of an acute inflammatory response to severe infection is considered. Regulation of the inflammatory response is crucial for restoring the patient to a healthy state. Therefore, an optimal control strategy given by a pro-inflammatory and anti-inflammatory drug treatment are derived. A study of controllability is also presented and the existence result is established. The optimality system composed of four differential equation and their corresponding adjoint equations are solved numerically. Simulation results are presented and different drug treatment strategies are discussed.