# American Institute of Mathematical Sciences

2008, 5(3): 485-504. doi: 10.3934/mbe.2008.5.485

## Modelling the immunopathogenesis of HIV-1 infection and the effect of multidrug therapy: The role of fusion inhibitors in HAART

 1 Department of Applied Mathematics, National University of Science and Technology, PO Box AC939 Ascot, Bulawayo 2 Department of Applied Biololgy, National University of Science and Technology, PO Box AC939 Ascot, Bulawayo

Received  October 2007 Revised  May 2008 Published  June 2008

There is currently tremendous effort being directed at developing potent, highly active antiretroviral therapies that can effectively control HIV- 1 infection without the need for continuous, lifelong use of these drugs. In the ongoing search for powerful antiretroviral agents that can affect sustained control for HIV infection, mathematical models can help in assessing both the correlates of protective immunity and the clinical role of a given drug regimen as well as in understanding the efficacy of drug therapies administered at different stages of the disease. In this study, we develop a new mathematical model of the immuno-pathogenesis of HIV-1 infection, which we use to assess virological responses to both intracellular and extracellular antiretroviral drugs. We first develop a basic mathematical model of the immuno-pathogenesis of HIV-1 infection that incorporates three distinct stages in the infection cycle of HIV-1: entry of HIV-1 into the cytoplasm of CD4+ T cells, transcription of HIV-1 RNA to DNA within CD4+ T cells, and production of HIV-1 viral particles within CD4+ T cells. Then we extend the basic model to incorporate the effect of three major categories of anti-HIV-1 drugs: fusion/entry inhibitors (FIs), reverse transcriptase inhibitors (RTIs), and protease inhibitors (PIs). Model analysis establishes that the actual drug efficacy of FIs, γ and of PIs, κ is the same as their effective efficacies while the effective drug efficacy for the RTIs, γ εis dependent on the rate of transcription of the HIV-1 RNA to DNA, and the lifespan of infected CD4+ T cells where virions have only entered the cytoplasm and that this effective efficacy is less than the actual efficacy, ε. Our studies suggest that, of the three anti-HIV drug categories (FIs, RTIs, and PIs), any drug combination of two drugs that includes RTIs is the weakest in the control of HIV-1 infection.
Citation: Gesham Magombedze, Winston Garira, Eddie Mwenje. Modelling the immunopathogenesis of HIV-1 infection and the effect of multidrug therapy: The role of fusion inhibitors in HAART. Mathematical Biosciences & Engineering, 2008, 5 (3) : 485-504. doi: 10.3934/mbe.2008.5.485
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