Modeling CD4+ T cells and CTL response in HIV-1 infection with antiretroviral therapy

Sutimin Sutimin, Sunarsih Sunarsih, R. Heru Tjahjana


The majority of an immune system infected by HIV (Human Immunodeficiency Virus) is CD4+ T cells. The HIV-1 transmission through cell to cell of CD4+ T cells supports the productive infection. On the other hand, infected CD4+ T cells stimulate cytotoxic T-lymphocytes cells to control HIV-1 infection. We develop and analyze a mathematical model incorporating the infection process through cell to cell contact of CD4+ T cells, CTL compartment and the combination of RTI and PI treatments. By means of the alternative reproduction ratio, it is analyzed the stability criteria and the existence of endemic equilibrium. Numerical simulations are presented to study the implication of the combination of RTI and PI therapy. The results indicate that RTI drug shows more significant effect in reducing HIV-1 infection compared to PI drug.


HIV-1, CD4+ T cells, CTL cells, RTI, PI.

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F. Hladik, P. Sakchalathorn, L. Ballweber, G. Lentz, M. Fialkow, D. Eschenbach, M. J. McElrath. Initial Events in Establishing

Vaginal Entry and Infection by Human Immunodeficiency Virus Type-1. Immunity, 26(2): 257–270, 2007.

Q. J. Sattentau. Cell-to-Cell Spread of Retroviruses. Viruses, 2(6): 1306–1321, 2010.

C. Jolly. Cell-to-cell transmission of retroviruses: Innate immunity and interferon-induced restriction factors. Virology, 411(2): 251–259, 2011.

A. Del Portillo, J. Tripodi, V. Najfeld, D. Wodarz, D. N. Levy, B. K. Chen, Multiploid inheritance of HIV-1 during cell-to-cell infection. J.Virol, 85(14): 7169–7176, 2011.

N. Gulzar and K. F. T. Copeland. CD8+ T-Cells: Function and Response to HIV Infection. Current HIV Research, 2:23–37,2004.

F. Kirchhoff. HIV Life Cycle: Overview. Encyclopedia of AIDS, pp. 1–9, 2013.

N. N. Klimas, A. O. Koneru and M. A. Fletcher. Overview of HIV. Psychosomatic Medicine, 70: 523–530, 2008.

D. N. Vatakis, S. Kim, N. Kim, S. A. Chow, and J. A. Zack. Human Immunodeficiency Virus Integration Efficiency and Site Selection in Quiescent CD4+ T Cells. J. Virology, pp. 8925–8928, 2009.

W. J. Swiggard, U. ODoherty, D. McGain, D. Jeyakumar and M. H. Malim. Long HIV type 1 reverse transcripts can accumulate stably within resting CD4+ T cells while short ones are degraded. AIDS Res. Hum. Retrovir., 20: 285–295, 2004.

P. K. Srivastava, M. Banerjee and P. Chandra. Modeling the Drug Therapy for HIV Infection. J. Biol. Sys., 17(2): 213–223, 2009.

F. Chirove, Sutimin, E. Soewono and N. Nuraini. Analysis of combined Langerhans and CD4+ T cells HIV infection. SIAM J. Appl. Math., 74(4): 1174–1193, 2014.

Sutimin, F. Chirove, E. Soewono, N. Nuraini and L. B. Suromo. Ultra A model incorporating combined RTIs and PIs therapy during early HIV-1 infection. Math. Bio., 285: 102–111, 2017.

Sutimin, N. Nuraini, F. Chirove and L. B. Suromo. Modelling Multiple Dosing with Drug Holiday in Antiretroviral Treatment on HIV-1 Infection. J. Math. Fund. Sci., 49(1): 1–17, 2017.

N. Tarfulea, A. Blink, E. Nelson, Jr. D. Turpin. A CTL-Inclusive Mathematical Model for Antiretroviral Treatment of HIV Infection. Int. J. Biomath., 4(1): 1–22, 2011.

N. E. Tarfulea. A Mathematical Model for CTL Effect on a Latently Infected Cell Inclusive HIV Dynamics and Treatment. AIP Conf. Proc. 1895, 070005, 4(1): 1–10, 2017.

O. Diekmann and J. A. P. Heesterbeek. Mathematical Epidemiology of Infectious Diseases: Model Building, Analysis and Interpretation. John Wiley & Sons, Chichester, UK. 2000.

M. Sugaya, K. Lor, R. A. Koup, D. C. Douek, A. Blauvelt. HIV-Infected Langerhans Cells Preferentially Transmit Virus to Proliferating Autologous CD4+ Memory T Cells Located within Langerhans Cell-T Cell Clusters. The J Immunol., 172(4): 2219–2224, 2004.

A. S. Perelson, D. E. Kirschner and R. D. Boer. Dynamics of HIV infection of CD4+T cells. Math. Bio., 114(1): 81–125, 1993.

D. Kirschner. Using mathematics to understand HIV immune dynamics. Notices Amer. Math. Soc., 43: 191–202, 1996.

Z. Wang and X. Liu. A chronic viral infection model with immune impairment. J. Theoret. Biol., 249: 532–542, 2007.

B. M. Adams, H. T. Banks, M. Davidian, H. D. Kwon, H. T. Tran, S. N. Wynne and E. S. Rosenberg. HIV dynamics: Modeling, data analysis, and optimal treatment protocols. J.Comput. Appl. Math., 184: 10–49, 2005.

R. Culshaw and S. Ruan. A delay-differential equation model of HIV infection of CD4+ T-cells,. J. Math. Biosci., 165: 27–39, 2000.

D. Wodarz, R. M. May and M. A. Nowak. The role of antigen-independent persistence of memory cytotoxic T lymphocytes. Int. Immunol., 12: 467–477, 2000.

S. Bonhoeffer, J. M. Coffin and M. A. Nowak. Human Immunodeficiency Virus drug therapy and virus load. J. Virol., 71: 3275–3278, 1997.

L. Rong, Z. Feng and A. S. Perelson. Emergence of HIV-1 drug resistance during antiretroviral treatment. Bull. Math. Biol., 69: 2027–2060, 2007.

P. S. Rivadeneira, C. H. Moog, G. B. Stan, C. Brunet, F. Raffi, V. Ferr, V. Costanza, M. J. Mhawej, F. Biafore, D. A. Ouattara, D. Ernst, R. Fonteneau and X. Xia. Mathematical Modeling of HIV Dynamics after Antiretroviral Therapy Initiation: A Review. Biores Open Access., 3(5): 233–241, 2014.



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