Optimal control of a delayed hepatitis B viral infection model with cytotoxic T-lymphocyte and antibody responses

Abstract

The dynamics of a model describing the hepatitis B viral infection model with cytotoxic T-lymphocyte and antibody responses is studied in this paper. The model consists of a system of differential equations describing the interaction between hepatocytes, the free virus and the immune responses. Both the treatment and the intracellular delay are incorporated into the model. Existence, positivity and boundedness of solutions are investigated. Also, the existence of the optimal control pair is established and the Pontryagin’s minimum principle is used to characterize these optimal controls. The optimal controls represent the efficiency of drug treatment in inhibiting viral production and preventing new infections. The optimality system is derived and solved numerically using the forward and backward difference approximation. The obtained results show that the optimal treatment strategies reduce the viral load and then increase the uninfected hepatocytes, this improves the patient life quality.