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Bulletin of Mathematical Sciences and Applications
Volume 9

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# A Delay Differential Equation Model of HIV Infection, with Therapy and CTL Response

## Abstract:

In this work we investigate a new mathematical model that describes the interactions betweenCD4+ T cells, human immunodeﬁciency virus (HIV), immune response and therapy with two drugs.Also an intracellular delay is incorporated into the model to express the lag between the time thevirus contacts a target cell and the time the cell becomes actively infected. The model dynamicsis completely deﬁned by the basic reproduction number R0. If R0 ≤ 1 the disease-free equilibriumis globally asymptotically stable, and if R0 > 1, two endemic steady states exist, and their localstability depends on value of R0. We show that the intracellular delay aﬀects on value of R0 becausea larger intracellular delay can reduce the value of R0 to below one. Finally, numerical simulationsare presented to illustrate our theoretical results.

## Info:

Periodical:
Bulletin of Mathematical Sciences and Applications (Volume 9)
Pages:
53-68
Citation:
B. El Boukari and N. Yousﬁ, "A Delay Differential Equation Model of HIV Infection, with Therapy and CTL Response", Bulletin of Mathematical Sciences and Applications, Vol. 9, pp. 53-68, 2014
Online since:
Aug 2014
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References:

S. Bonhoeffer, M. Rembiszewski, G. M. Ortiz and D. F. Nixon (2000). Risks and benefits of structured antiretroviral drug therapy interruptions in HIV-1 infection. AIDS , 14, 2313-2322.

S. M. Ciupe, B. L. Bivort, D. Bortz, Nelson. P (2006), Estimates of kinetic parameters from HIV patient data during primary infection through the eyes of three different models, Math Biosci 200: 1-27.

R. V. Culshaw, S. Ruan, (2000). A delay-dierential equation model of HIV infection of CD4+T-cells. Math Biosci 165: 27-39.

B. EL Boukari, K. Hattaf, N. Yousfi, (2013). Modeling the Therapy of HIV Infection with CTL Response and Cure Rate . Int. J. Ecol. Econ. Stat 28: 1-17.

I. S. Gradshteyn, I. M. Ryzhik, (2000). Routh-Hurwitz Theorem, in Tables of Integrals, Series, and Products, 6th ed. San Diego, CA: Academic Press, 1076.

J. Hale and S. M. Verduyn Lunel, (1993) Introduction to Functional Differential Equations, Springer- Verlag, New York.

K. Hattaf and N. Yousfi, (2011). Dynamics of HIV Infection Model with Therapy and Cure Rate, International Journal of tomography and Statistics, 74-80.

P. Nelson, A. Perelson, (2002). Mathematical analysis of delay differential equation models of HIV-1 infection, Mathematical Biosciences 179 73-94.

M. A. Nowak, C. R. M. Bangham, (1996). Population dynamics of Immune Responses to Persitent Viruses, Science, 272, 74-79.

A. S. Perelson, D. E. Kirschner, and R. D. Boer, (1993). Dynamics of HIV infection of CD4+ T-cells Math Biosci 114: 81-125.

A. Perelson, A. Neumann, M. Markowitz, J. Leonard and D. Ho, (1996). HIV-1 dynamics in vivo: Virion clearance rate, infected cell life-span, and viral generation time, Science, 271 , 1582-1586.

A. Perelson, P. Nelson, (1999). Mathematical Analysis of HIV dynamics in vivo, SIAM Rev., 41 3-44.

P. K. Srivastava, M. Banerjee, P. Chandra, (2010). A primary infection model for HIV and immune response with two discrete time delays, Diff. Equ. Dyn. Syst, 18(4): 385-399.

L. Wang and M. Y. Li, Mathematical analysis of the global dynamics of a model for HIV infection of CD4+ T cells, Math. Biosci., 200 (2006), 44-57.

N. Yousfi, K. Hattaf and A. Tridane, (2011). Modeling the adaptative immune response in HBV infection, J. Math. Bio., 63(5): 933-957.

H. Zhu and X. Zou, (2008). Impact of delays in cell infection and virus production on HIV1 dy- namics. Mathematical Medicine and Biology, 25, 99-112.

H. Zhu and X. Zou, (2009). Dynamics of a HIV-1 Infection Model With Cell-Mediated Immune Response And Intracellular Delay, Discrete And Continuous Dynamical Systems Series B, Vol. 12, N o2, 511-524.