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 |
|---|---|
| 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 |
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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)
Cite this
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 journal › Article
}
TY - JOUR
T1 - Long term dynamics in a mathematical model of HIV-1 infection with delay in different variants of the basic drug therapy model
AU - Roy, Priti Kumar
AU - Chatterjee, Amar Nath
AU - Greenhalgh, David
AU - Khan, Qamar J A
PY - 2013/6
Y1 - 2013/6
N2 - 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.
AB - 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.
KW - Asymptotic stability
KW - CD4 T cells
KW - Cell lysis
KW - Cytotoxic T-lymphocyte
KW - HIV-1
KW - Reverse transcriptase inhibitor
KW - Time delay
KW - Time series solutions
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UR - http://www.scopus.com/inward/citedby.url?scp=84872034701&partnerID=8YFLogxK
U2 - 10.1016/j.nonrwa.2012.10.021
DO - 10.1016/j.nonrwa.2012.10.021
M3 - Article
VL - 14
SP - 1621
EP - 1633
JO - Nonlinear Analysis: Real World Applications
JF - Nonlinear Analysis: Real World Applications
SN - 1468-1218
IS - 3
ER -