A delayed HIV-1 infection model with Beddington-DeAngelis functional response

Nonlinear Dynamics

Volumn 62, Issue 1-2, 2010, Pages 67-72

  Wang, Xia ^a   Tao, Youde ^a,b   Song, Xinyu ^a  

^a XINYANG NORMAL UNIVERSITY   (China)

^b Beijing Institute of Information Control   (China)

Author keywords

Beddington DeAngelis; HIV 1 infection; Intracellular delay; Stability

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; DYNAMICS; MECHANICAL ENGINEERING;

BEDDINGTON-DE ANGELIS FUNCTIONAL RESPONSE; BEDDINGTON-DEANGELIS; FUNCTIONAL RESPONSE; GLOBAL STABILITY; HIV-1 INFECTIONS; INTRACELLULAR DELAY; LOCAL STABILITY;

MATHEMATICAL MODELS;

EID: 84861737820     PISSN: 0924090X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11071-010-9699-1     Document Type: Article

References (18)

1. Culshaw, R.V., Ruan, S.G.: A delay-differential equation model of HIV infection of CD4+ T-cells. Math. Biosci. 165, 27-39 (2000).
2. Culshaw, R.V., Ruan, S.G., Webb, G.: A mathematical model of cell-to-cell spread of HIV-1 that includes a time delay. J. Math. Biol. 46, 425-444 (2003).
3. Dumrongpokaphan, T., Lenbury, Y., Ouncharoen, R., Xu, Y.S.: An intracellular delay-differential equation model of the HIV infection and immune control. Math. Model. Nat. Phenom. Epidemiol. 2, 75-99 (2007).
4. Katri, P., Ruan, S.G.: Dynamics of human T-cell lymphotropic virus I (HTLV-I) infection of CD4+ T-cells. C. R. Biol. 327, 1009-1016 (2004).
5. Liu, W.-M.: Nonlinear oscillations in models of immune responses to persistent viruses. Theor. Popul. Biol. 52(3), 224-230 (1997).
6. Murase, A., Sasaki, T., Kajiwara, T.: Stability analysis of pathogen-immune interaction dynamics. J. Math. Biol. 51, 247-267 (2005).
7. Nowak, Martin A., Bangham, Charles R.M.: Population dynamics of immune responses to persistent viruses. Science 272, 74-79 (1996).
8. Perelson, A.S., Kirschner, D.E., Boer, R.D.: Dynamics of HIV infection of CD4+ T cells. Math. Biosci. 114, 81-125 (1993).
9. Perelson, A.S., Nelson, P.W.: Mathematical models of HIV dynamics in vivo. SIAM Rev. 41, 3-44 (1999).
10. Zhu, H.Y., Zou, X.F.: Impact of delays in cell infection and virus production on HIV-1 dynamics. Math. Med. Biol. 25, 99-112 (2008).
11. Beddington, J.R.: Mutual interference between parasites or predators and its effect on searching efficiency. J. Anim. Ecol. 44, 331-340 (1975).
12. DeAngelis, D.L., Goldstein, R.A., O'Neill, R.V.: A model for trophic interaction. Ecology 56, 881-892 (1975).
13. Li, D., Ma, W.B.: Asymptotic properties of a HIV-1 infection model with time delay. J. Math. Anal. Appl. 335, 683-691 (2007).
14. Nagurno, M.: Uber die Lage der Integralkurven gewonlicher differential Gleichungen. Proc. Phys. Math. Soc. Jpn. 24, 551-559 (1942).
15. Hale, J.: Theory of Functional Differential Equations. Springer, New York (1997).
16. Kuang, Y.: Delay Differential Equations with Applications in Population Dynamics. Academic Press, San Diego (1993).
17. Busenberg, S., Cooke, K.L.: Vertically Transmitted Diseases, Models and Dynamics. Biomathematics, vol. 23. Springer, New York (1993).
18. Beretta, E., Kuang, Y.: Geometric stability switch criteria in delay differential systems with delay dependent parameters. SIAM J. Math. Anal. 33, 1144-1165 (2002).