Stability analysis and cauchy matrix of a mathematical model of hepatitis b virus with control on immune system near neighborhood of equilibrium free point

Mathematical models are useful tools to describe the dynamics of infection and predict the role of possible drug combinations. In this paper, we present an analysis of a hepatitis B virus (HBV) model including cytotoxic T lymphocytes (CTL) and antibody responses, under distributed feedback control, expressed as an integral form to predict the effect of a combination treatment with interleukin-2 (IL-2). The method presented in this paper is based on the symmetry properties of Cauchy matrices C(t, s), which allow us to construct and analyze the stability of corresponding integro-differential systems.