Dynamic behavior in a HIV infection model for the delayed immune response

WSEAS Transactions on Mathematics

Volumn 10, Issue 11, 2011, Pages 398-407

  Wang, Yongzhao ^a   Huang, Dongwei ^a   Zhang, Shuangde ^b   Liu, Hongjie ^a  

^a TIANJIN POLYTECHNIC UNIVERSITY   (China)

^b MEDICAL COLLEGE OF CHINESE PEOPLE'S ARMED POLICE FORCES   (China)

Author keywords

Delayed immune response; Global stability; Logistic proliferation

Indexed keywords

BIFURCATION PARAMETER; DYNAMIC BEHAVIORS; DYNAMICS OF SYSTEM; GLOBAL ASYMPTOTIC STABILITY; GLOBAL STABILITY; HIV INFECTION MODEL; HIV MODELS; IMMUNE RESPONSE; NUMERICAL SIMULATING; PROLIFERATION RATE; T CELLS; TIME DELAYED;

ASYMPTOTIC STABILITY; IMMUNOLOGY;

HOPF BIFURCATION;

EID: 80055045617     PISSN: 11092769     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (20)

1. M. A. Nowak and R. M. May, Mathematical biology of HIV infection: antigenic variation and diversity threshold, Math. Biosci, No.106 ,1991, pp.1-21.
2. A. S. Perelson, A. U. Neumann, M. Markowitz, J. M. Leonard and D. D. Ho, HIV-1 dynamics in vivo: virion clearance rate, infected cell life-span, and viral generation time, Science, No.271 ,1996,pp.1582-1599.
3. Z. Hu, X. Liu, H. Wang and W. Ma, Analysis of the dynamics of a delayed HIV pathogenesis model, J. Comput.Appl Math, No.234 , 2010, pp.461-476.
4. A. S. Perelson, D. E.Nelson Kirschner and R. De Boer. Dynamics of HIV Infection of CD4+ T-cells. Math Biosci, No.114 ,1993,pp.81-125.
5. P. W. Nelson and A. S. Perelson, Mathematical analysis of delay differential equation models of HIV-1 infection. Math Biosci, No.179 , 2002, pp. 73-94. (Pubitemid 34686428)
6. M. Chen and H. Zhu, Dynamics of a HIV infection model with delay in immune response, J. Biomath, No. 24(4), 2009, pp.624-634.
7. M. A. Nowak and C. R. M. Bangham, Population dynamics of immune response to persistent viruses, Science , No.272 , 1996, pp. 74-49.
8. K. Wang, W. Wang and X. Liu, Global stability in a viral infection model with lytic and non-lytic immune response in viral infections. J. Comput.Appl Math, No.51 ,2007, pp.1593-1610.
9. Y. Ji, L. Min, Y. Zheng and Y. Su, A virus infection model with periodic immune response and nonlinear CTL response. Math Comput Simul, No.80, 2010, pp. 2309-2316.
10. C. Bartholdy, J. P. Christensen, D. Wodarz and A. R.Thomsen, Persistent virus infection despite chronic cytotoxic T-lymphocyte activation in Gamma interferon-deficient mice infected with lymphocytic choriomeningitis virus. J. Virol, 2000, pp. 10304-10311.
11. D. Wodarz, J. P. Christensen and A. R. Thomsen, The importance of lytic and nolytic immune responses in virus infections. Trends Immunol, No.23 ,2002,pp. 194-200. (Pubitemid 34260935)
12. K. Wang, W. Wang, H. Pang and X. Liu, Complex dynamic behavior in a viral model with delayed immune response. Physica D, No.226,2007,pp. 197-208. (Pubitemid 46185615)
13. A. A. Canabarro, I. M. Gleria and M. L. Lyra, Periodic solutions and chaos in a non-linear model for the delayed cellular immune response .Physica A., No. 342,2004, pp.234-241.
14. Y. Wang, Y. Zhou ,J. Wang and J. Heffernan, Oscillatory viral dnamics in a delayed HIV pathogenesis model. Math Biosci, No. 219 , 2009, pp.104-112.
15. P. De Leenheer and H. L. Smith, Virus dynamics: A global analysis, SIAM J. Appl. Math . No.63 , 2003, pp. 1313-1327.
16. J. K. Hale, Theory of Functional Differential Equations, Springer-Verlag, NewYork,1997.
17. J. P. LaSalle, The stability of dynamical systems, in: Regional Conference Series in Applied Mathematics, SIAM, Philadelphia, PA, 1976.
18. E. Beretta and Y. Kuang, Geometric stability switch criteria in delay differential systems with delay dependent parameters. SIAM J, Math Anal, No.33 ,2002,pp.1144-1165.
19. J.Li,Z.Ma, Stability switches in a class of characteristic equations with delay-dependent parameters, Nonlinear Analysis: Real World Applications, No.5 ,2004,pp. 389-408.
20. J. Hale and S. V. Lunel, Introduction to Functional Differential Equations, Springer, New York , 1993.