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

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

66 Citations (Scopus)


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. Bonhoeffer et al. (1997) [1], 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 T-Lymphocyte (CTL) and in the stimulation of CTL and analyse 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.

Original languageEnglish
Pages (from-to)1621-1633
Number of pages13
JournalNonlinear Analysis: Real World Applications
Issue number3
Publication statusPublished - Jun 2013


  • Asymptotic stability
  • CD4 T cells
  • Cell lysis
  • Cytotoxic T-lymphocyte
  • HIV-1
  • Reverse transcriptase inhibitor
  • Time delay
  • Time series solutions

ASJC Scopus subject areas

  • Analysis
  • General Engineering
  • Economics, Econometrics and Finance(all)
  • Computational Mathematics
  • Applied Mathematics


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