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. 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 language | English |
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Pages (from-to) | 1621-1633 |
Number of pages | 13 |
Journal | Nonlinear Analysis: Real World Applications |
Volume | 14 |
Issue number | 3 |
DOIs | |
Publication status | Published - Jun 2013 |
Keywords
- 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
- Applied Mathematics
- Computational Mathematics
- Engineering(all)
- Medicine(all)
- Economics, Econometrics and Finance(all)