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Analysis of HIV models with two time delays
- Source :
- Journal of Biological Dynamics, Vol 11, Iss 0, Pp 40-64 (2017)
- Publication Year :
- 2016
-
Abstract
- Time delays can affect the dynamics of HIV infection predicted by mathematical models. In this paper, we studied two mathematical models each with two time delays. In the first model with HIV latency, one delay is the time between viral entry into a cell and the establishment of HIV latency, and the other delay is the time between cell infection and viral production. We defined the basic reproductive number and showed the local and global stability of the steady states. Numerical simulations were performed to evaluate the influence of time delays on the dynamics. In the second model with HIV immune response, one delay is the time between cell infection and viral production, and the other delay is the time needed for the adaptive immune response to emerge to control viral replication. With two positive delays, we obtained the stability crossing curves for the model, which were shown to be a series of open-ended curves.
- Subjects :
- 0301 basic medicine
Time delays
Time Factors
Basic Reproduction Number
HIV Infections
Biology
Virus Replication
01 natural sciences
Models, Biological
immune response
03 medical and health sciences
Control theory
Viral entry
Virus latency
medicine
Humans
0101 mathematics
Latency (engineering)
lcsh:QH301-705.5
latency
lcsh:Environmental sciences
Ecology, Evolution, Behavior and Systematics
lcsh:GE1-350
stability crossing curve
Ecology
Mathematical model
stability
Models, Theoretical
HIV infection
Acquired immune system
medicine.disease
characteristic quasipolynomial
Virus Latency
010101 applied mathematics
030104 developmental biology
lcsh:Biology (General)
Viral replication
Immunology
HIV-1
Basic reproduction number
Subjects
Details
- ISSN :
- 17513766
- Volume :
- 11
- Issue :
- sup1
- Database :
- OpenAIRE
- Journal :
- Journal of biological dynamics
- Accession number :
- edsair.doi.dedup.....6554fbfc04fcbea659325aa39b61e2ed