Long term dynamics in a mathematical model of HIV-1 infection with delay in different variants of the basic drug therapy model

Priti Kumar Roy, Amar Nath Chatterjee, David Greenhalgh, Qamar J A Khan

Research output: Contribution to journalArticle

46 Citations (Scopus)

Abstract

Infection with HIV-1, degrading the human immune system and recent advances of drug therapy to arrest HIV-1 infection, has generated considerable research interest in the area. Sebastian Bonhoeffer et al. [2], introduced a population model representing long term dynamics of HIV infection in response to available drug therapies. We consider a similar type of approximate model incorporating time delay in the process of infection on the healthy T cells which, in turn, implies inclusion of a similar delay in the process of viral replication. The model is studied both analytically and numerically. We also include a similar delay in the killing rate of infected CD4+ T cells by Cytotoxic TLymphocyte (CTL) and in the stimulation of CTL and analyze two resulting models numerically.

The models with no time delay present have two equilibria: one where there is no infection and a non-trivial equilibrium where the infection can persist. If there is no time delay then the non-trivial equilibrium is locally asymptotically stable. Both our analytical results (for the first model) and our numerical results (for all three models) indicate that introduction of a time delay can destabilize the non-trivial equilibrium. The numerical results indicate that such destabilization occurs at realistic time delays and that there is a threshold time delay beneath which the equilibrium with infection present is locally asymptotically stable and above which this equilibrium is unstable and exhibits oscillatory solutions of increasing amplitude.
LanguageEnglish
Pages1621-1633
Number of pages13
JournalNonlinear Analysis: Real World Applications
Volume14
Issue number3
DOIs
Publication statusPublished - Jun 2013

Fingerprint

Drug therapy
Therapy
HIV Infections
Infection
HIV-1
Time Delay
Drugs
Theoretical Models
Time delay
Mathematical Model
Mathematical models
Drug Therapy
Term
T-cells
Asymptotically Stable
Model
T-Lymphocytes
Numerical Results
HIV Infection
Oscillatory Solution

Keywords

  • HIV-1
  • time series solutions
  • cell lysis
  • time delay
  • asymptotic stability
  • reverse transcriptase inhibitor
  • cytotoxic T-lymphocyte
  • CD4+ T cells

Cite this

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title = "Long term dynamics in a mathematical model of HIV-1 infection with delay in different variants of the basic drug therapy model",
abstract = "Infection with HIV-1, degrading the human immune system and recent advances of drug therapy to arrest HIV-1 infection, has generated considerable research interest in the area. Sebastian Bonhoeffer et al. [2], introduced a population model representing long term dynamics of HIV infection in response to available drug therapies. We consider a similar type of approximate model incorporating time delay in the process of infection on the healthy T cells which, in turn, implies inclusion of a similar delay in the process of viral replication. The model is studied both analytically and numerically. We also include a similar delay in the killing rate of infected CD4+ T cells by Cytotoxic TLymphocyte (CTL) and in the stimulation of CTL and analyze two resulting models numerically.The models with no time delay present have two equilibria: one where there is no infection and a non-trivial equilibrium where the infection can persist. If there is no time delay then the non-trivial equilibrium is locally asymptotically stable. Both our analytical results (for the first model) and our numerical results (for all three models) indicate that introduction of a time delay can destabilize the non-trivial equilibrium. The numerical results indicate that such destabilization occurs at realistic time delays and that there is a threshold time delay beneath which the equilibrium with infection present is locally asymptotically stable and above which this equilibrium is unstable and exhibits oscillatory solutions of increasing amplitude.",
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Long term dynamics in a mathematical model of HIV-1 infection with delay in different variants of the basic drug therapy model. / Roy, Priti Kumar; Chatterjee, Amar Nath; Greenhalgh, David; Khan, Qamar J A .

In: Nonlinear Analysis: Real World Applications, Vol. 14, No. 3, 06.2013, p. 1621-1633.

Research output: Contribution to journalArticle

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