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Abstract and Applied Analysis
Volume 2014, Article ID 586035, 6 pages
http://dx.doi.org/10.1155/2014/586035
Research Article

Dynamics Analysis of a Viral Infection Model with a General Standard Incidence Rate

Department of Mathematics, Beijing Technology and Business University, Beijing 100048, China

Received 23 May 2014; Accepted 20 August 2014; Published 14 October 2014

Academic Editor: Peixuan Weng

Copyright © 2014 Yu Ji and Muxuan Zheng. 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.

Linked References

  1. P. de Leenheer and H. L. Smith, “Virus dynamics: a global analysis,” SIAM Journal on Applied Mathematics, vol. 63, no. 4, pp. 1313–1327, 2003. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  2. S. Lewin, T. Walters, and S. Locarnini, “Hepatitis B treatment: rational combination chemotherapy based on viral kinetic and animal model studies,” Antiviral Research, vol. 55, no. 3, pp. 381–396, 2002. View at Publisher · View at Google Scholar · View at Scopus
  3. M. A. Nowak and R. M. May, Virus Dynamics, Oxford University Press, Oxford, UK, 2000. View at MathSciNet
  4. A. S. Perelson and P. W. Nelson, “Mathematical analysis of HIV-1 dynamics in vivo,” SIAM Review, vol. 41, no. 1, pp. 3–44, 1999. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  5. L. Min, Y. Su, and Y. Kuang, “Mathematical analysis of a basic virus infection model with application to HBV infection,” The Rocky Mountain Journal of Mathematics, vol. 38, no. 5, pp. 1573–1585, 2008. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  6. S. A. Gourley, Y. Kuang, and J. D. Nagy, “Dynamics of a delay differential equation model of hepatitis B virus infection,” Journal of Biological Dynamics, vol. 2, no. 2, pp. 140–153, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  7. T. Wang, Z. Hu, F. Liao, and W. Ma, “Global stability analysis for delayed virus infection model with general incidence rate and humoral immunity,” Mathematics and Computers in Simulation, vol. 89, pp. 13–22, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  8. L. M. Cai and X. Z. Li, “Analysis of a SEIV epidemic model with a nonlinear incidence rate,” Applied Mathematical Modelling, vol. 33, no. 7, pp. 2919–2926, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  9. K. Hattaf, N. Yousfi, and A. Tridane, “Mathematical analysis of a virus dynamics model with general incidence rate and cure rate,” Nonlinear Analysis: Real World Applications, vol. 13, no. 4, pp. 1866–1872, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  10. Z. P. Wang and R. Xu, “Stability and Hopf bifurcation in a viral infection model with nonlinear incidence rate and delayed immune response,” Communications in Nonlinear Science and Numerical Simulation, vol. 17, no. 2, pp. 964–978, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  11. K. Wang, A. Fan, and A. Torres, “Global properties of an improved hepatitis B virus model,” Nonlinear Analysis. Real World Applications, vol. 11, no. 4, pp. 3131–3138, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  12. X. Song and A. U. Neumann, “Global stability and periodic solution of the viral dynamics,” Journal of Mathematical Analysis and Applications, vol. 329, no. 1, pp. 281–297, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  13. Z. X. Hu, J. J. Zhang, H. Wang, W. Ma, and F. Liao, “Dynamics analysis of a delayed viral infection model with logistic growth and immune impairment,” Applied Mathematical Modelling, vol. 38, no. 2, pp. 524–534, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  14. J. A. Yorke and W. P. London, “Recurrent outbreaks of measles, chickenpox and mumps. II. Systematic differences in contact rates and stochastic effects,” The American Journal of Epidemiology, vol. 98, no. 6, pp. 469–482, 1973. View at Google Scholar · View at Scopus
  15. W. M. Liu, H. W. Hethcote, and S. A. Levin, “Dynamical behavior of epidemiological models with nonlinear incidence rates,” Journal of Mathematical Biology, vol. 25, no. 4, pp. 359–380, 1987. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  16. M. Y. Li and L. C. Wang, “Global stability in some SEIR epidemic models,” in Mathematical Approaches for Emerging and Reemerging Infectious Diseases: Models, Methods, and Theory, vol. 126 of The IMA Volumes in Mathematics and Its Applications, pp. 295–311, Springer, New York, NY, USA, 2002. View at Publisher · View at Google Scholar · View at MathSciNet
  17. G. Butler and P. Waltman, “Persistence in dynamical systems,” Journal of Differential Equations, vol. 63, no. 2, pp. 255–263, 1986. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  18. M. Y. Li, J. R. Graef, L. Wang, and J. Karsai, “Global dynamics of a SEIR model with varying total population size,” Mathematical Biosciences, vol. 160, no. 2, pp. 191–213, 1999. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus