Discrete and Continuous Dynamical Systems - Series B (DCDS-B)

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

Pages: 229 - 240, Volume 8, Issue 1, July 2007      doi:10.3934/dcdsb.2007.8.229

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Rachid Ouifki - SACEMA, DST/NRF Centre of Excellence in Epidemiological Modelling and Analysis, Stellenbosch University, 19 Jonkershoek Road, Stellenbosch 7600, South Africa (email)
Gareth Witten - Department of Mathematics and Applied Mathematics, University of Cape Town, Rondebosch 7701, Cape Town, South Africa (email)

Abstract: 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:  HIV, treatment, differential equation, delay, stability.
Mathematics Subject Classification:  Primary: 58F15, 58F17; Secondary: 53C35.

Received: October 2005;      Revised: March 2006;      Available Online: April 2007.