American Institute of Mathematical Sciences

Advanced
July  2007, 8(1): 229-240. doi: 10.3934/dcdsb.2007.8.229

A model of HIV-1 infection with HAART therapy and intracellular delays

Rachid Ouifki 1, and  Gareth Witten 2,

1. 

SACEMA, DST/NRF Centre of Excellence in Epidemiological Modelling and Analysis, Stellenbosch University, 19 Jonkershoek Road, Stellenbosch 7600, South Africa
2. 

Department of Mathematics and Applied Mathematics, University of Cape Town, Rondebosch 7701, Cape Town, South Africa

Received  October 2005 Revised  March 2006 Published  April 2007

We consider a model of HIV-1 infection with triple drug therapy (HAART) and three delays: the first delay represents the time between the infection and the viral production, the second is associated with the loss of target cells by infection, and the third represents the time for the newly produced virions to become infectious. We show that the incorporation of these delays improves the critical efficacy of the treatment, and destabilizes the infected steady state or leads to an infected steady state with more healthy cells and less infected cells and viruses. Also, we considered the periodic treatment case. We analyze the stability of the viral free steady state and derive an effective strategy for reducing the viral load.
Keywords: stability., differential equation, delay, HIV, treatment.
Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C3.
Citation: Rachid Ouifki, Gareth Witten. A model of HIV-1 infection with HAART therapy and intracellular delays. Discrete and Continuous Dynamical Systems - B, 2007, 8 (1) : 229-240. doi: 10.3934/dcdsb.2007.8.229
[1]

Urszula Foryś, Jan Poleszczuk. A delay-differential equation model of HIV related cancer--immune system dynamics. Mathematical Biosciences & Engineering, 2011, 8 (2) : 627-641. doi: 10.3934/mbe.2011.8.627
[2]

Esther Chigidi, Edward M. Lungu. HIV model incorporating differential progression for treatment-naive and treatment-experienced infectives. Mathematical Biosciences & Engineering, 2009, 6 (3) : 427-450. doi: 10.3934/mbe.2009.6.427
[3]

Bao-Zhu Guo, Li-Ming Cai. A note for the global stability of a delay differential equation of hepatitis B virus infection. Mathematical Biosciences & Engineering, 2011, 8 (3) : 689-694. doi: 10.3934/mbe.2011.8.689
[4]

Songbai Guo, Wanbiao Ma. Global behavior of delay differential equations model of HIV infection with apoptosis. Discrete and Continuous Dynamical Systems - B, 2016, 21 (1) : 103-119. doi: 10.3934/dcdsb.2016.21.103
[5]

Pham Huu Anh Ngoc. Stability of nonlinear differential systems with delay. Evolution Equations and Control Theory, 2015, 4 (4) : 493-505. doi: 10.3934/eect.2015.4.493
[6]

Ellina Grigorieva, Evgenii Khailov, Andrei Korobeinikov. An optimal control problem in HIV treatment. Conference Publications, 2013, 2013 (special) : 311-322. doi: 10.3934/proc.2013.2013.311
[7]

Eugen Stumpf. On a delay differential equation arising from a car-following model: Wavefront solutions with constant-speed and their stability. Discrete and Continuous Dynamical Systems - B, 2017, 22 (9) : 3317-3340. doi: 10.3934/dcdsb.2017139
[8]

Leonid Berezansky, Elena Braverman. Stability of linear differential equations with a distributed delay. Communications on Pure and Applied Analysis, 2011, 10 (5) : 1361-1375. doi: 10.3934/cpaa.2011.10.1361
[9]

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
[10]

Nara Bobko, Jorge P. Zubelli. A singularly perturbed HIV model with treatment and antigenic variation. Mathematical Biosciences & Engineering, 2015, 12 (1) : 1-21. doi: 10.3934/mbe.2015.12.1
[11]

Shohel Ahmed, Abdul Alim, Sumaiya Rahman. A controlled treatment strategy applied to HIV immunology model. Numerical Algebra, Control and Optimization, 2018, 8 (3) : 299-314. doi: 10.3934/naco.2018019
[12]

Jan Čermák, Jana Hrabalová. Delay-dependent stability criteria for neutral delay differential and difference equations. Discrete and Continuous Dynamical Systems, 2014, 34 (11) : 4577-4588. doi: 10.3934/dcds.2014.34.4577
[13]

Cuilian You, Yangyang Hao. Stability in mean for fuzzy differential equation. Journal of Industrial and Management Optimization, 2019, 15 (3) : 1375-1385. doi: 10.3934/jimo.2018099
[14]

Jinliang Wang, Lijuan Guan. Global stability for a HIV-1 infection model with cell-mediated immune response and intracellular delay. Discrete and Continuous Dynamical Systems - B, 2012, 17 (1) : 297-302. doi: 10.3934/dcdsb.2012.17.297
[15]

Yukihiko Nakata. Existence of a period two solution of a delay differential equation. Discrete and Continuous Dynamical Systems - S, 2021, 14 (3) : 1103-1110. doi: 10.3934/dcdss.2020392
[16]

P. Dormayer, A. F. Ivanov. Symmetric periodic solutions of a delay differential equation. Conference Publications, 1998, 1998 (Special) : 220-230. doi: 10.3934/proc.1998.1998.220
[17]

Nasser Sweilam, Fathalla Rihan, Seham AL-Mekhlafi. A fractional-order delay differential model with optimal control for cancer treatment based on synergy between anti-angiogenic and immune cell therapies. Discrete and Continuous Dynamical Systems - S, 2020, 13 (9) : 2403-2424. doi: 10.3934/dcdss.2020120
[18]

Tomás Caraballo, José Real, T. Taniguchi. The exponential stability of neutral stochastic delay partial differential equations. Discrete and Continuous Dynamical Systems, 2007, 18 (2&3) : 295-313. doi: 10.3934/dcds.2007.18.295
[19]

Leonid Shaikhet. Stability of equilibriums of stochastically perturbed delay differential neoclassical growth model. Discrete and Continuous Dynamical Systems - B, 2017, 22 (4) : 1565-1573. doi: 10.3934/dcdsb.2017075
[20]

Samuel Bernard, Fabien Crauste. Optimal linear stability condition for scalar differential equations with distributed delay. Discrete and Continuous Dynamical Systems - B, 2015, 20 (7) : 1855-1876. doi: 10.3934/dcdsb.2015.20.1855

2020 Impact Factor: 1.327

Tools

Metrics

  • PDF downloads (75)
  • HTML views (0)
  • Cited by (2)

Other articles
by authors

[Back to Top]

Copyright © 2022 American Institute of Mathematical Sciences | Privacy Policy