Skip to main content

Advertisement

Log in

Global stability of endemic equilibrium point of basic virus infection model with application to HBV infection

  • Published:
Journal of Systems Science and Complexity Aims and scope Submit manuscript

Abstract

In this paper, the authors first show that if R 0 ≤ 1, the infection free steady state is globally attractive by using approaches different from those given by Min, et al.(2008). Then the authors prove that if R 0 > 1, the endemic steady state is also globally attractive. Finally, based on a patient’s clinical HBV DNA data of anti-HBV infection with drug lamivudine, the authors establish an ABVIM. The numerical simulations of the ABVIM are good in agreement with the clinical data.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. L. Q. Min, Y. M. Su, and Y. Kuang, Mathematical analysis of a basic model of virus infection with application to HBV infection, Rocky Mountain J. Math., 2008, 38(5): 1573–1584.

    Article  MATH  MathSciNet  Google Scholar 

  2. M. A. Nowak and R. M. May, Viral Dynamics, Oxford University Press, Oxford, 2000.

    Google Scholar 

  3. A. Perelson, A. Neumann, M. Markowitz, et al., HIV-1 dynamics in vivo: Virion clearance rate, infected cell life-span, and viral generation time, Science, 271(5255): 1582–1586.

  4. A. Neumann, N. Lam, H. Dahari, et al., Hepatitis C viral dynamics in vivo and antiviral efficacy of the interferon-therapy, Science, 1998, 282(5386): 103–107.

    Article  Google Scholar 

  5. S. Zeuzem, J. M. Schmidt, J. H. Lee, et al., Effect of interferon alfa on the dynamics of hepatitis C virus turnover in vivo, J. Hepatology, 1996, 23(2): 366–371.

    Google Scholar 

  6. M. A. Feitelson and J. D. Larkin, New animal models for hepatitis B and C, Ilar J., 2001, 42(2): 127–138.

    Google Scholar 

  7. P. D. Leenheer and H. L. Smith, Virus dynamics: A global analysis, SIAM J. Appl. Math., 2003, 63(4): 1313–1327.

    Article  MATH  MathSciNet  Google Scholar 

  8. G. K. Lau, T. Piratvisuth, K. X. Luo, et al., Peginterferon Alfa-2a, Lamivudine, and the Combination for HBeAg-Positive Chronic Hepatitis B, N. Engl. J. Med., 2005, 352(26): 2682–2695.

    Article  Google Scholar 

  9. S. A. Gourley, Y. Kuang, and J. D. Nagy, Dynamics of a delay differential model of hepatitis B virus, J. Biological Dynamics, 2008, 2(2): 140–153.

    Article  MATH  MathSciNet  Google Scholar 

  10. X. Y. Song and A. Neumann, Global stability and periodic solution of the viral dynamics, J. Math. Anal. Appl., 2007, 329(1): 281–297.

    Article  MATH  MathSciNet  Google Scholar 

  11. H. L. Smith, Monotone Dynamical Systems, AMS, Providence, RI, 1995.

    MATH  Google Scholar 

  12. J. S. Muldowney, Compound matrices and ordinary differential equations, Rocky Mountain J. Math., 1990, 20(4): 857–872.

    Article  MATH  MathSciNet  Google Scholar 

  13. M. A. Nowak, S. Bonhoeffer, A. M. Hill, et al., Viral dynamics in hepatitis B virus infection, Proc. Natl. Acad. Sci. USA, 1996, 93(9): 4398–4402.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Yu Zheng.

Additional information

This research is supported by the National Natural Science Foundations of China under Grant No. 60674059, the 11th 5-Year Plan Key Research Project of China under Grant No. 2004BA721A03, the China National Key Special Project for the Preventions and Cures of Important Infectious Diseases under Grant No. 2008ZX10005-006.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zheng, Y., Min, L., Ji, Y. et al. Global stability of endemic equilibrium point of basic virus infection model with application to HBV infection. J Syst Sci Complex 23, 1221–1230 (2010). https://doi.org/10.1007/s11424-010-8467-0

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11424-010-8467-0

Key words

Navigation