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Mathematical Biosciences and Engineering

2005, Volume 2, Issue 2: 363-380. doi: 10.3934/mbe.2005.2.363
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A mathematical model for treatment-resistant mutations of HIV

  • 1.
    American Institute of Mathematics, 360 Portage Avenue, Palo Alto, CA 94306
  • 2.
    Department of Mathematics, Harvey Mudd College, 1250 N. Dartmouth Avenue, Claremont, CA 91711
  • Received: 01 September 2004 Accepted: 29 June 2018 Published: 01 March 2005

  • MSC : 37N25.

  • In this paper, we propose and analyze a mathematical model, in the form of a system of ordinary differential equations, governing mutated strains of human immunodeficiency virus (HIV) and their interactions with the immune system and treatments. Our model incorporates two types of resistant mutations: strains that are not responsive to protease inhibitors, and strains that are not responsive to reverse transcriptase inhibitors. It also includes strains that do not have either of these two types of resistance (wild-type virus) and strains that have both types. We perform our analysis by changing the system of ordinary differential equations (ODEs) to a simple single-variable ODE, then identifying equilibria and determining stability. We carry out numerical calculations that illustrate the behavior of the system. We also examine the effects of various treatment regimens on the development of treatment-resistant mutations of HIV in this model.

    Citation: Helen Moore, Weiqing Gu. A mathematical model for treatment-resistant mutations of HIV[J]. Mathematical Biosciences and Engineering, 2005, 2(2): 363-380. doi: 10.3934/mbe.2005.2.363

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  • In this paper, we propose and analyze a mathematical model, in the form of a system of ordinary differential equations, governing mutated strains of human immunodeficiency virus (HIV) and their interactions with the immune system and treatments. Our model incorporates two types of resistant mutations: strains that are not responsive to protease inhibitors, and strains that are not responsive to reverse transcriptase inhibitors. It also includes strains that do not have either of these two types of resistance (wild-type virus) and strains that have both types. We perform our analysis by changing the system of ordinary differential equations (ODEs) to a simple single-variable ODE, then identifying equilibria and determining stability. We carry out numerical calculations that illustrate the behavior of the system. We also examine the effects of various treatment regimens on the development of treatment-resistant mutations of HIV in this model.


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    1. Faraimunashe Chirove, Edward M. Lungu, Effects of replicative fitness on competing HIV strains, 2013, 113, 03032647, 28, 10.1016/j.biosystems.2013.04.001
    2. Hee-Dae Kwon, Optimal treatment strategies derived from a HIV model with drug-resistant mutants, 2007, 188, 00963003, 1193, 10.1016/j.amc.2006.10.071
    3. S. DE LILLO, M. DELITALA, M. C. SALVATORI, MODELLING EPIDEMICS AND VIRUS MUTATIONS BY METHODS OF THE MATHEMATICAL KINETIC THEORY FOR ACTIVE PARTICLES, 2009, 19, 0218-2025, 1405, 10.1142/S0218202509003838
    4. Helen Moore, How to mathematically optimize drug regimens using optimal control, 2018, 45, 1567-567X, 127, 10.1007/s10928-018-9568-y
    5. O. Sharomi, A.B. Gumel, Dynamical analysis of a multi-strain model of HIV in the presence of anti-retroviral drugs, 2008, 2, 1751-3758, 323, 10.1080/17513750701775599
    6. Peter E. Kloeden, Christian Pötzsche, 2013, Chapter 1, 978-3-319-03079-1, 3, 10.1007/978-3-319-03080-7_1
    7. Hee-Dae Kwon, Jeehyun Lee, Sung-Dae Yang, Optimal control of an age-structured model of HIV infection, 2012, 219, 00963003, 2766, 10.1016/j.amc.2012.09.003
    8. Hee-Dae Kwon, Jeehyun Lee, Myoungho Yoon, An age-structured model with immune response of HIV infection: Modeling and optimal control approach, 2014, 19, 1553-524X, 153, 10.3934/dcdsb.2014.19.153
    9. Yanping Ma, Yeona Kang, Angelica Davenport, Jennifer Mawunyo Aduamah, Kathryn Link, Katharine Gurski, 2024, Chapter 2, 978-3-031-58515-9, 9, 10.1007/978-3-031-58516-6_2
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