American Institute of Mathematical Sciences

Advanced
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

Gesham Magombedze 1, , Winston Garira 1, and  Eddie Mwenje 2,

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.
Keywords: mathematical modelling., Human immunodeficiency virus (HIV), highly active antiretroviral therapy (HAART), Fusion inhibitors (FIs).
Mathematics Subject Classification: 92D3.
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
[1]

Rachid Ouifki, Gareth Witten. A model of HIV-1 infection with HAART therapy and intracellular delays. Discrete & Continuous Dynamical Systems - B, 2007, 8 (1) : 229-240. doi: 10.3934/dcdsb.2007.8.229
[2]

Nirav Dalal, David Greenhalgh, Xuerong Mao. Mathematical modelling of internal HIV dynamics. Discrete & Continuous Dynamical Systems - B, 2009, 12 (2) : 305-321. doi: 10.3934/dcdsb.2009.12.305
[3]

Tyson Loudon, Stephen Pankavich. Mathematical analysis and dynamic active subspaces for a long term model of HIV. Mathematical Biosciences & Engineering, 2017, 14 (3) : 709-733. doi: 10.3934/mbe.2017040
[4]

Federico Papa, Francesca Binda, Giovanni Felici, Marco Franzetti, Alberto Gandolfi, Carmela Sinisgalli, Claudia Balotta. A simple model of HIV epidemic in Italy: The role of the antiretroviral treatment. Mathematical Biosciences & Engineering, 2018, 15 (1) : 181-207. doi: 10.3934/mbe.2018008
[5]

Yun Tian, Yu Bai, Pei Yu. Impact of delay on HIV-1 dynamics of fighting a virus with another virus. Mathematical Biosciences & Engineering, 2014, 11 (5) : 1181-1198. doi: 10.3934/mbe.2014.11.1181
[6]

Juan Pablo Aparicio, Carlos Castillo-Chávez. Mathematical modelling of tuberculosis epidemics. Mathematical Biosciences & Engineering, 2009, 6 (2) : 209-237. doi: 10.3934/mbe.2009.6.209
[7]

Baba Issa Camara, Houda Mokrani, Evans K. Afenya. Mathematical modeling of glioma therapy using oncolytic viruses. Mathematical Biosciences & Engineering, 2013, 10 (3) : 565-578. doi: 10.3934/mbe.2013.10.565
[8]

Gesham Magombedze, Winston Garira, Eddie Mwenje. Modelling the human immune response mechanisms to mycobacterium tuberculosis infection in the lungs. Mathematical Biosciences & Engineering, 2006, 3 (4) : 661-682. doi: 10.3934/mbe.2006.3.661
[9]

Zahra Al Helal, Volker Rehbock, Ryan Loxton. Modelling and optimal control of blood glucose levels in the human body. Journal of Industrial & Management Optimization, 2015, 11 (4) : 1149-1164. doi: 10.3934/jimo.2015.11.1149
[10]

Geoffrey Beck, Sebastien Imperiale, Patrick Joly. Mathematical modelling of multi conductor cables. Discrete & Continuous Dynamical Systems - S, 2015, 8 (3) : 521-546. doi: 10.3934/dcdss.2015.8.521
[11]

Oliver Penrose, John W. Cahn. On the mathematical modelling of cellular (discontinuous) precipitation. Discrete & Continuous Dynamical Systems - A, 2017, 37 (2) : 963-982. doi: 10.3934/dcds.2017040
[12]

Ariel D. Weinberger, Alan S. Perelson. Persistence and emergence of X4 virus in HIV infection. Mathematical Biosciences & Engineering, 2011, 8 (2) : 605-626. doi: 10.3934/mbe.2011.8.605
[13]

Bing Li, Yuming Chen, Xuejuan Lu, Shengqiang Liu. A delayed HIV-1 model with virus waning term. Mathematical Biosciences & Engineering, 2016, 13 (1) : 135-157. doi: 10.3934/mbe.2016.13.135
[14]

Praveen Kumar Gupta, Ajoy Dutta. Numerical solution with analysis of HIV/AIDS dynamics model with effect of fusion and cure rate. Numerical Algebra, Control & Optimization, 2019, 9 (4) : 393-399. doi: 10.3934/naco.2019038
[15]

Cameron J. Browne, Sergei S. Pilyugin. Minimizing $\mathcal R_0$ for in-host virus model with periodic combination antiviral therapy. Discrete & Continuous Dynamical Systems - B, 2016, 21 (10) : 3315-3330. doi: 10.3934/dcdsb.2016099
[16]

Helen Moore, Weiqing Gu. A mathematical model for treatment-resistant mutations of HIV. Mathematical Biosciences & Engineering, 2005, 2 (2) : 363-380. doi: 10.3934/mbe.2005.2.363
[17]

Xiaodan Sun, Yanni Xiao, Zhihang Peng. Modelling HIV superinfection among men who have sex with men. Mathematical Biosciences & Engineering, 2016, 13 (1) : 171-191. doi: 10.3934/mbe.2016.13.171
[18]

Shengqiang Liu, Lin Wang. Global stability of an HIV-1 model with distributed intracellular delays and a combination therapy. Mathematical Biosciences & Engineering, 2010, 7 (3) : 675-685. doi: 10.3934/mbe.2010.7.675
[19]

Liumei Wu, Baojun Song, Wen Du, Jie Lou. Mathematical modelling and control of echinococcus in Qinghai province, China. Mathematical Biosciences & Engineering, 2013, 10 (2) : 425-444. doi: 10.3934/mbe.2013.10.425
[20]

Roderick Melnik, B. Lassen, L. C Lew Yan Voon, M. Willatzen, C. Galeriu. Accounting for nonlinearities in mathematical modelling of quantum dot molecules. Conference Publications, 2005, 2005 (Special) : 642-651. doi: 10.3934/proc.2005.2005.642

2018 Impact Factor: 1.313

Tools

Metrics

  • PDF downloads (5)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2019 American Institute of Mathematical Sciences