Optimal control of a delayed system subject to mixed control-state constraints with application to a within-host model of hepatitis virus B

This paper deals with the problem of optimal control of a delayed differential equation system subject to mixed control-state constraints with application to a within-host model of hepatitis B virus (HBV). Our method consists to transform the optimal control problem of a delayed differential equation with mixed control-state constraints to a nondelayed problem in order to derive necessary optimality conditions. This theory is applied to a deterministic HBV model with two constant delays. We derive conditions under which is optimal to eradicate HBV within the body of a host. Through numerical simulations, we found that the best control strategy to reduce the HBV infection is the combination of treatment in blocking new infection and treatment in inhibiting viral production.