A differential equation model of HIV infection of CD4+ T-cells with cure rate

Journal of Mathematical Analysis and Applications

Volumn 342, Issue 2, 2008, Pages 1342-1355

  Zhou, Xueyong ^a   Song, Xinyu ^a,b   Shi, Xiangyun ^a  

^a XINYANG NORMAL UNIVERSITY   (China)

^b HENAN UNIVERSITY   (China)

Author keywords

Globally asymptotical stability; HIV; Periodic solution

Indexed keywords

EID: 40649105716     PISSN: 0022247X     EISSN: 10960813     Source Type: Journal    
DOI: 10.1016/j.jmaa.2008.01.008     Document Type: Article

References (20)

1. De Boer R.J., and Perelson A.S. Target cell limited and immune control models of HIV infection: A comparison. J. Theoret. Biol. 190 (1998) 201-214
2. Kepler T.B., and Perelson A.S. Cyclic re-entry of germinal center B cells and the efficiency of affinity maturation. Immunol. Today 14 (1993) 412-415
3. Percus J.K., Percus O.E., and Perelson A.S. Predicting the size of the T-cell receptor and antibody combining region from consideration of efficient self-nonself discrimination. Proc. Natl. Acad. Sci. USA 90 (1993) 1691-1695
4. McKeithan T.W. Kinetic proofreading in T-cell receptor signal transduction. Proc. Natl. Acad. Sci. USA 92 (1995) 5042-5046
5. McLean A.R., Rosado M.M., Agenes F., Vasconcellos R., and Freitas A.A. Resource competition as a mechanism for B cell homeostasis. Proc. Natl. Acad. Sci. USA 94 (1997) 5792-5797
6. Song X.Y., and Neumann A.U. Global stability and periodic solution of the viral dynamics. J. Math. Anal. Appl. 329 1 (2007) 281-297
7. Lloyd A.L. The dependence of viral parameter estimates on the assumed viral life cycle: Limitations of studies of viral load data. Proc. R. Soc. Lond. Ser. B 268 (2001) 847-854
8. Li D., and Ma W. Asymptotic properties of a HIV-1 infection model with time delay. J. Math. Anal. Appl. 335 1 (2007) 683-691
9. McLean A.R., and Kirkwood T.B.L. A model of human immunodeficiency virus infection in T helper cell clones. J. Theoret. Biol. 147 (1990) 177-203
10. McLean A.R., and Nowak M.A. Models of interaction between HIV and other pathogens. J. Theoret. Biol. 155 (1992) 69-102
11. Mittler J.E., Sulzer B., Neumann A.U., and Perelson A.S. Influence of delayed viral production on viral dynamics in HIV-1 infected patients. Math. Biosci. 152 (1998) 143-163
12. Perelson A.S., Essunger P., Cao Y., Vesanen M., Hurley A., Saksela K., Markowitz M., and Ho D.D. Decay characteristics of HIV-1-infected compartments during combination therapy. Nature 387 (1997) 188-191
13. Kuang Y. Delay Differential Equations with Applications in Population Dynamics (2004), Academic Press, London
14. Gantmacher F.R. The Theory of Matrices (1959), Chelsea Publ. Co., New York
15. Hale J.K., and Waltman P. Persistence in infinite-dimensional systems. SIAM J. Math. Anal. 20 (1989) 388-396
16. Smith H.L. Monotone Dynamical Systems, an Introduction to the Theory of Competitive and Cooperative Systems. Math. Surveys Monogr. vol. 41 (1995), Amer. Math. Soc., Providence, RI
17. Li M.Y., and Wang L. Global stability in some SEIR models. IMA Math. Appl. 126 (2002) 295-311
18. Zhu H.R., Smith H.L., and Hirsch M.W. Stable periodic orbits for a class of three dimensional competitive systems. J. Differential Equations 110 (1994) 143-156
19. Perelson A.S., and Nelson P.W. Mathematical analysis of HIV-1 dynamics in vivo. SIAM Rev. 41 (1999) 3-44
20. + T-cells. J. Korean Math. Soc. 42 5 (2005) 1071-1086