Stability and Bifurcation Analysis for a Delay Differential Equation of Hepatitis B Virus Infection

Abstract

The stability and bifurcation analysis for a delay differential equation of hepatitis B virus infection is investigated. We show the existence of nonnegative equilibria under some appropriated conditions. The existence of the Hopf bifurcation with delay $\tau$ at the endemic equilibria is established by analyzing the distribution of the characteristic values. The explicit formulae which determine the direction of the bifurcations, stability, and the other properties of the bifurcating periodic solutions are given by using the normal form theory and the center manifold theorem. Numerical simulation verifies the theoretical results.