Abstract:
Virus dynamics models are useful in interpreting and predicting the change in viral load
over the time and the effect of treatment in emerging viral infections like HIV/AIDS, hepatitis B
virus (HBV). We propose a mathematical model involving the role of total immune response (innate,
CTL, and humoral) and treatment for productively infected cells and free virus to understand the
dynamics of virus–host interactions. A threshold condition for the extinction or persistence of
infection, i.e. basic reproductive number, in the presence of immune response (RI) is established.
We study the global stability of virus-free equilibrium and interior equilibrium using LaSalle’s
principle and Lyapunov’s direct method. The global stability of virus-free equilibrium ensures the
clearance of virus from the body, which is independent of initial status of subpopulations. Central
manifold theory is used to study the behavior of equilibrium points