Dynamics of HBV infection model with DNA-containing capsids, logistic hepatocyte growth and adaptive immune response

Abstract

In this paper, the model describes the interactions between the hepatocytes, the free hepatitis B virus (HBV) with DNA-containing capsids, and the adaptive immune response represented by the cytotoxic T lymphocytes (CTL) cells and the anti-bodies with a delay-differential equation and logistic hepatocyte growth. We show the existence, positivity and boundedness of solution and we analyse the existence and the stability of the disease free equilibrium and the endemic equilibrium points. Also, the existence of the optimal control pair is established and Pontryagin’s minimum principle is used to characterize the efficiency of drug treatment in inhibiting viral production and preventing new infections. The obtained results are discussed numerically to show that the optimal treatment strategies reduce the viral load and then increase the uninfected hepatocytes, this improves the patient’s quality of life.