Immune therapy using optimal control with L1 type objective

Treatment of pathogenic infection is formulated as an optimal control problem with an L
¹
type objective. Being unable to regulate the resulting inflammatory response can be detrimental for the affected patient. A strategy given by a pro-inflammatory and anti-inflammatory mediator drug treatment is derived. We apply maximum principle and the optimality system composed of four differential equation and their corresponding adjoint equations are solved numerically. Simulation results are discussed for two commun critical cases.