Modeling the dynamics of HIV and \(CD4^{+}\)T cells during primary infection. (English) Zbl 1181.37122

Summary: A mathematical model for the dynamics of HIV primary infection is proposed and analysed for the stability of infected state. Further, as there is a time delay for infected \(CD4^{+}\) T cells to become actively infected, a model is proposed to consider this time delay. The local stability of the delay model is discussed and results are shown numerically. It is found that the delay has no effect on the dynamics of HIV in the proposed model.


37N25 Dynamical systems in biology
92D30 Epidemiology
92C37 Cell biology
Full Text: DOI


[1] Nowak, M.A.; May, R.M., Virus dynamics, (2000), Oxford University Press · Zbl 1101.92028
[2] Perelson, A.S.; Nelson, P.W., Mathematical analysis of HIV-1 dynamics in vivo, SIAM rev., 41, 3-44, (1999) · Zbl 1078.92502
[3] Perelson, A.S., Modelling the interaction of the immune system with HIV, () · Zbl 0683.92001
[4] Perelson, A.S.; Kirschner, D.E.; Boer, R.De, Dynamics of HIV infection of \(C D 4^+\) T cells, Math. biosci., 114, 81-125, (1993) · Zbl 0796.92016
[5] Rong, L.; Gilchrist, M.A.; Feng, Z.; Perelson, A.S., Modeling within host HIV-1 dynamics and the evolution of drug resistance: trade offs between viral enzyme function and drug susceptibility, J. theoret. biol., 247, 804-818, (2007)
[6] Zack, J.A.; Arrigo, S.J.; Weitsman, S.R.; Go, A.S.; Haislip, A.; Chen, I.S., HIV-1 entry into quiescent primary lymphocytes: molecular analysis reveals a labile latent viral structure, Cell, 61, 213-222, (1990)
[7] Zack, J.A.; Haislip, A.M.; Krogstad, P.; Chen, I.S., Incompletely reverse-transcribed human immunodeficiency virus type 1 genomes in quiescent cells can function as intermediates in the retroviral cycle, J. virol., 66, 1717-1725, (1992)
[8] Essunger, P.; Perelson, A.S., Modeling HIV infection of \(C D 4^+\) T-cell subpopulations, J. theoret. biol., 170, 367-391, (1994)
[9] Herz, A.V.M.; Bonhoeer, S.; Anderson, R.M.; May, R.M.; Nowak, M.A., Viral dynamics in vivo: limitations on estimates of intracellular delay and virus decay, Proc. natl. acad. sci. USA, 93, 7247-7251, (1996)
[10] LaSalle, J.P., The stability of dynamical systems, () · Zbl 0153.40602
[11] Freedman, H.I.; Tang, M.X.; Ruan, S.G., Uniform persistence and flows near a closed positively invariant set, J. dynam. diff. equ., 6, 583-600, (1994) · Zbl 0811.34033
[12] Butler, G.J.; Waltman, P., Persistence in dynamical systems, Proc. amer. math. soc., 96, 425-430, (1986)
[13] Li, M.Y.; Muldowney, J.S., A geometric approach to the global-stability problems, SIAM J. math. anal., 27, 1070-1083, (1996) · Zbl 0873.34041
[14] Coppel, W.A., Stability and asymptotic behavior of differential equations, (1965), Health Boston · Zbl 0154.09301
[15] Muldowney, J.S., Compound matrices and ordinary differential equations, Rocky mountain J. math., 20, 857-872, (1990) · Zbl 0725.34049
[16] Dieudonne, J., Foundations of modern analysis, (1960), Academic Press New York · Zbl 0100.04201
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