Journal of Applied Mathematics
Volume 2013 (2013), Article ID 875783, 15 pages
http://dx.doi.org/10.1155/2013/875783
Research Article

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

Xinchao Yang,1 Xiju Zong,2 Xingong Cheng,2 and Zhenlai Han3

1School of Medical and Life Science, University of Jinan, Jinan, Shandong 250022, China
2School of Electrical Engineering, University of Jinan, Jinan, Shandong 250022, China
3School of Science, University of Jinan, Jinan, Shandong 250022, China

Received 29 July 2012; Accepted 27 December 2012

Academic Editor: Yongkun Li

Copyright © 2013 Xinchao Yang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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 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.