Nonlinear Dynamics

, Volume 67, Issue 1, pp 723–734 | Cite as

The importance of immune responses in a model of hepatitis B virus

  • Jianhua Pang
  • Jing-an CuiEmail author
  • Jing Hui
Original Paper


In this paper, the dynamical behavior of a hepatitis B virus model with CTL immune responses is studied. Analyzing the model, we show that the virus-free equilibrium is globally asymptotically stable if the basic reproductive ratio of virus is less than one and the endemic equilibrium is locally asymptotically stable if the basic reproductive ratio is greater than one. When the basic reproductive ratio is greater than one, the system is uniformly persistent, which means the virus is endemic. Mathematical analysis and numerical simulations show that the CTL immune responses play a significant and decisive role in eradication of disease. The study and information derived from this model may have an important impact on treatment protocols of hepatitis B virus in the future.


Viral dynamics Basic reproductive ratio Cytolytic mechanisms Noncytolytic mechanisms Permanence 


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Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.School of Mathematical SciencesNanjing Normal UniversityNanjingP.R. China
  2. 2.Department of Information and ComputingGuangxi University of TechnologyLiuzhouP.R. China
  3. 3.School of ScienceBeijing University of Civil Engineering and ArchitectureBeijingP.R. China
  4. 4.Mechanical Engineering DepartmentGuangxi University of TechnologyLiuzhouP.R. China

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