Modelling Multiple Dosing with Drug Holiday in Antiretroviral Treatment on HIV-1 Infection

Sutimin Sutimin, Nuning Nuraini, Faraimunashe Chirove, Lisyani Budipradigda Suromo


A within-host mathematical model to describe the dynamics of target cells and viral load in early HIV-1 infection was developed, which incorporates a combination of RTI and PI treatments by using a pharmacokinetics model. The local stability of uninfected steady state for the model was determined using an alternative threshold. The pharmacokinetics model was employed to estimate drug efficacy in multiple drug dosing. The effect of periodic drug efficacy of pharmacokinetic type on outcome of HIV-1 infection was explored under various treatment interruptions. The effectiveness of treatment interruption was determined according to the time period of the drug holidays. The results showed that long drug holidays lead to therapy failure. Under interruption of treatments combining RTI and PI therapy, effectiveness of the treatment requires a short duration of the drug holiday. 


CD4+T cells; drug holiday; HIV-1; Langerhans; pharmacokinetics

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Dragic, T., Litwin V, Allaway G.P., Martin E.R., Huang, Nagashima K.A., Cayanan C, Maddon P.J., Koup, R.A., Moore, J.P. & Paxton, W.A., HIV-1 Entry into CD4+ Cells is Mediated by the Chemokine Receptor CC-CKR-5, Nature, 381(6584), pp. 667-673, 1996.

Hladik, F., Sakchalathorn, P., Ballweber, L., Lentz, G., Fialkow, M., Eschenbach, D. & McElrath, M.J., Initial Events in Establishing Vaginal Entry and Infection by Human Immunodeficiency Virus Type-1, Immunity, 8(2), pp. 257-270, 2000.

Rong, L., Feng, Z. & Perelson, A.S., Emergence of HIV-1 Drug Resistance During Antiretroviral Treatment, Bull. Math. Biol., 69(6), pp. 2027-2060, 2007.

Ding, A.A. & Wu, H., Assessing Antiviral Potency of anti-HIV Therapies in-vivo by Comparing Viral Decay Rates in Viral Dynamic Models, Biostatistics, 2(1), pp. 13-29, 2001.

Kirschner, K.E. & Webb, G.F., A Mathematical Model of Combined Drug Therapy of HIV Infection, J. Theor. Med., 1(1), pp. 25-34, 1997.

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

De Leenheer, P., Within-Host Virus Models with Periodic Antiviral Therapy, Bull. Math. Biol., 71(1), pp. 189-210, 2009.

Tarfulea, N., A Mathematical Model for HIV Treatment with Time-varying Antiretroviral Therapy, Int. J. Comp. Math., 88(15), pp. 3217-3235, 2011.

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

Perelson, A.S. & Ribeiro, R.M., Modeling the Within-host Dynamics of HIV Infection, BMC Biology, 11(96), pp. 1-10, 2013.

Chirove, F., Sutimin, Soewono, E. & Nurainin N., Analysis of Combined Langerhans and CD4 T Cells HIV Infection, SIAM J. App. Math., 74(4), pp. 1174-1193, 2014.

Sutimin, Chirove, F., Soewono, E., Nuraini, N. & Lisyani, B.S., A Model Incorporating Combined RTIs and PIs Therapy During Early HIV-1 Infection, Mathematical Biosciences, 285, pp. 102-111, 2017.

Vikram, L., Singh, R.A., Sandeep, S., Tarun, J. & Mohan, D., Population Pharmacokinetics of Antiretroviral Agents: On Review, IRJP, 3(7), pp. 75-85, 2012.

Bonhoeffer, S., Rembiszewski, M., Ortiz, G.M. & Nixon, D.F., Risks and Benefits of Structured Antiretroviral Drug Therapy Interruptions in HIV-1 Infection, AIDS, 14(15), pp. 2313-2322, 2000.

Ju, R. & Uetrecht, F.M., Mechanism of Idiosyncratic Drug Reactions: Reactive Metabolites Formation, Protein Binding and the Regulation of the Immune System, Current Drug Metabolism, 3(4), pp. 367-377, 2002.

Pichler, W.J., The P-I Concept: Pharmacological Interaction of Drugs with Immune Receptors, World Allergy Organ J., 1(6), pp. 96-102, 2008.

Weber, J., The Pathogenesis of HIV-1 Infection, British Med. Bull., 58(1), pp. 61-72, 2001.

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

Dixit, N.M. & Perelson, A.S., Complex Patterns of Viral Load Decay under Antiretroviral Therapy: Influence of Pharmacokinetics and Intracellular Delay, J. Theor. Biol., 226(1), pp. 95-109, 2004.

Miron, R.E. & Smith, R.J., Modelling Imperfect Adherence to HIV Induction Therapy, BMC Infect. Dis., 10(6), pp. 1-16, 2010.

Benson, C.A., Perspective Structured Treatment Interruptions—New Findings, International AIDS Society-USA, 14(3), pp. 107-111, 2006.

Culshaw, R. & Ruan, S., A Delay-differential Equation Model of HIV Infection of CD4+ T-cells, Math. Biosci., 165(1), pp. 27-39, 2000.

Kamath, A.T., Henri, S., Battye, F., Tough, D.F. & Shortman, K., Developmental Kinetics and Lifespan of Dendritic Cells in Mouse Lymphoid Organs, Blood, 100(5), pp. 1734-1741, 2002.

Stafford, M.A., Corey, L., Cao, Y., Daar, E.S., Ho, D.D. & Perelson, A.S., Modeling Plasma Virus Concentration during Primary HIV Infection, J. Theor. Biol., 203(3), pp. 285-301, 2000.

Blauvelt, D., Blauvelt, A., Sugaya, M., Loré K., Koup, R.A. & Daniel, C., HIV-Infected Langerhans Cells Preferentially Transmit Virus to Proliferating Autologous CD4+ Memory T Cells Located within Langerhans Cell-to-cell Clusters, J. Immunol., 172(4), pp. 2219-2224, 2004.

Perelson, A.S., Kirschner, D.E. & De Boer, R., Dynamics of HIV Infection of CD4+T Cells, Math. Biosci., 114(1), pp. 81-125, 1993.

Kirschner, D., Using Mathematics to Understand HIV Immune Dynamics, Notices Amer. Math. Soc., 43(2), pp. 191-202, 1996.

Wang, Z. & Liu, X., A Chronic Viral Infection Model with Immune Impairment, J. Theor. Biol., 249(3), pp. 532-542, 2007.

Perelson, A.S. & Nelson, P.W., Mathematical Analysis of HIV-1 Dynamics In-vivo, SIAM Rev., 41(1), pp. 3-44, 1999.

Perelson, A.S., Neumann, A.U., Markowitz, M., Leonard, J.M. & Ho, D.D., HIV-1 Dynamics In-vivo: Virion Clearance Rate, Infected Cell Life-Span, and Viral Generation Time, Science, 271(5255), pp. 1582-1586, 1996.

Adams, B.M., Banks, H.T., Davidian, M., Kwon, H.D, Tran, H.T., Wynne, S.N. & Rosenberg, E.S., HIV Dynamics: Modeling, Data Analysis, and Optimal Treatment Protocols, J. Comput. Appl. Math., 184(1), pp. 10-49, 2005.

Dimitrov, D.S., Willey, R.L., Sato, H., Chang, L.J., Blumenthal, R. & Martin, M.A., Quantitation of Human Immunodeficiency Virus Type 1 Infection Kinetics, J. Virol., 67(4), pp. 2182-2190, 1993.

Haase, A.T., Henry, K., Zupancic, M., Sedgewick, G., Faust, R.A., Melroe, H., Cavert, W., Gebhard, K., Staskus, K., Zhang, Z.Q., Dailey, P.J., Balfour, H.H. Jr., Erice, A. & Perelson, A.S., Quantitative Image Analysis of HIV-1 Infection in Lymphoid Tissue, Science, 274(5289), pp. 985-989, 1996.

Mbogo, W.R., Luboobi, L.S. & Odhiambo, J.W., Stochastic Model for Langerhans Cells and HIV Dynamics In-vivo, ISRN App. Math., 2014, pp. 1-10, 2014.

Cameron, P., Pope, M., Granelli-Piperno, A. & Steinman, R.M., Dendritic Cells and The Replication of HIV-1, J. Leukoc. Biol., 59(2), pp. 158-171, 1996.

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

Horton, J.J., Allen, M.H. & MacDonald, D.M., An Assessment of Langerhans Cell Quantification in Tissue Sections, J. Am. Acad. Dermatol, 11(4), pp. 591-593, 1984

Knight, S.C., Macatonia, S.E. & Patterson, S., HIV I Infection of Dendritic Cells, Int. Rev. Immunol., 6(2-3), pp. 163-173, 1990.



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