American Institute of Mathematical Sciences

Advanced
2005, 2(4): 811-832. doi: 10.3934/mbe.2005.2.811

A two-strain HIV-1 mathematical model to assess the effects of chemotherapy on disease parameters

Tinevimbo Shiri 1, , Winston Garira 2, and  Senelani D. Musekwa 1,

1. 

Department of Applied Mathematics, National University of Science and Technology, P-O Box AC939 Ascot, Bulawayo, Zimbabwe, Zimbabwe
2. 

Department of Applied Mathematics, National University of Science and Technology, PO Box AC939 Ascot, Bulawayo, Zimbabwe

Received  July 2005 Revised  September 2005 Published  October 2005

Treatment of human immunodeficiency virus type 1 (HIV-1) infection during the symptomatic phase has significantly improved patient survival. We present a two-strain HIV mathematical model that captures the dynamics of the immune system and two HIV-1 variants under antiretroviral therapy. We explore the effects of chemotherapy on the dynamics of two viral strains and T lymphocytes with one mutant strain phenotypically resistant to drug effects. Model calculations show that there is a common pattern for CD4+ T cell count increase. There is a drastic increase of CD4+ T cells during the first few weeks of treatment, followed by a gradual increase, and these increases are strictly by clonal expansion of preexisting CD4+ T cells. Plasma HIV RNA dramatically decline to zero levels during the first week of drug administration. If drug efficacy is equal to or above a threshold efficacy, viral load remains at zero levels and if drug efficacy is less than the threshold efficacy, viral load gradually increases until it stabilizes. Viral rebound during treatment is entirely due to the recovery of CD4+ T cells. The results also reveal that there is a dynamic equilibrium between viral load and cytotoxic T lymphocyte (CTL) response in an infected individual during drug administration.
Keywords: HIV-1, viral load, mathematical model, chemotherapy, Cytotoxic T Lymphocytes..
Mathematics Subject Classification: 92D3.
Citation: Tinevimbo Shiri, Winston Garira, Senelani D. Musekwa. A two-strain HIV-1 mathematical model to assess the effects of chemotherapy on disease parameters. Mathematical Biosciences & Engineering, 2005, 2 (4) : 811-832. doi: 10.3934/mbe.2005.2.811
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