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

Authors:  P. Tchinda Mouofo, J.J. Tewa, B. Mewoli, S. Bowong

Abstract:
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.

Published in: Annual Reviews in Control  (Volume 37, Issue 2, April  2013)

Publisher: Elsevier

ISSN Information: 1367-5788

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

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