## Journal of Applied Mathematics

### 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.

#### Article information

Source
J. Appl. Math., Volume 2013 (2013), Article ID 875783, 15 pages.

Dates
First available in Project Euclid: 14 March 2014

https://projecteuclid.org/euclid.jam/1394807870

Digital Object Identifier
doi:10.1155/2013/875783

Mathematical Reviews number (MathSciNet)
MR3032269

Zentralblatt MATH identifier
1266.92059

#### Citation

Yang, Xinchao; Zong, Xiju; Cheng, Xingong; Han, Zhenlai. Stability and Bifurcation Analysis for a Delay Differential Equation of Hepatitis B Virus Infection. J. Appl. Math. 2013 (2013), Article ID 875783, 15 pages. doi:10.1155/2013/875783. https://projecteuclid.org/euclid.jam/1394807870

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