Properties of Stability and Local Hopf Bifurcation for an HBV Model with Two Delays

Abstract

This paper studies a mathematical model of Hepatitis B Virus (HBV) infection with two time delays, which considers the effect of lytic and non-lytic mechanisms in the Cytotoxic T Lymphocyte (CTL) immune response. First, global asymptotic stability conditions of the infection-free equilibrium point \(E_{0}\) and the immune-free equilibrium point \(E_{1}\) are discussed. Next, by choosing \(\tau _{1}\) and \(\tau _{2}\) as the bifurcation parameter, sufficient conditions for the local stability and the existence of Hopf bifurcation with respect to \(\tau _{1}\) and \(\tau _{2}\) are established. Last, a simulation example is employed to illustrate the proposed theoretical results.