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Discrete Dynamics in Nature and Society
Volume 2010, Article ID 182340, 21 pages
Research Article

Asymptotic Properties of a Hepatitis B Virus Infection Model with Time Delay

Institute of Applied Mathematics, Shijiazhuang Mechanical Engineering College, No. 97 Heping West Road, Shijiazhuang 050003, China

Received 14 February 2010; Accepted 21 August 2010

Academic Editor: Juan J. Nieto

Copyright © 2010 Xiaohong Tian and Rui Xu. 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.


A hepatitis B virus infection model with time delay is discussed. By analyzing the corresponding characteristic equations, the local stability of each of the feasible equilibria of the model is studied. By using comparison arguments, it is proved that if the basic reproduction ratio is less than unity, the infection-free equilibrium is globally asymptotically stable. If the basic reproduction ratio is greater than unity, by means of an iteration technique, sufficient conditions are derived for the global asymptotic stability of the virus-infected equilibrium. Numerical simulations are carried out to illustrate the theoretical results.