Mathematical modeling of HBV with the antiviral therapy for the immunocompromised patients

Abstract

In this paper, we study the dynamical behaviour of HBV infection model with antiviral therapy and CTL immune response. The model is given by a system of four ordinary differential equations with discrete time delay which describes the time between infection and the immune response. The existence and stability/unstability of the equilibrium points without treatment are proved with respect to the time delay and the basic reproduction number is estimated. The conditions of occurrence of Hopf bifurcation at the endemic steady state are established when the delay crosses some critical value by using the delay as a parameter of bifurcation. By incorporating interferon-α (IFN) and nucleotside analogs (NAs) treatments, the disappearance of oscillations and appearance of new equilibrium point with maximal value of uninfected cells and minimal value of effector cells and vanishing values of virus and infected cells are investigated via optimality control. Numerical illustrations are given to support theoretical results.