Viral dynamics model with CTL immune response incorporating antiretroviral therapy

Yan Wang, Yicang Zhou, Fred Brauer, Jane M. Heffernan

Research output: Contribution to journalArticle

50 Citations (Scopus)

Abstract

We present two HIV models that include the CTL immune response, antiretroviral therapy and a full logistic growth term for uninfected CD4+ T-cells. The difference between the two models lies in the inclusion or omission of a loss term in the free virus equation. We obtain critical conditions for the existence of one, two or three steady states, and analyze the stability of these steady states. Through numerical simulation we find substantial differences in the reproduction numbers and the behaviour at the infected steady state between the two models, for certain parameter sets. We explore the effect of varying the combination drug efficacy on model behaviour, and the possibility of reconstituting the CTL immune response through antiretroviral therapy. Furthermore, we employ Latin hypercube sampling to investigate the existence of multiple infected equilibria.

Original languageEnglish (US)
Pages (from-to)901-934
Number of pages34
JournalJournal of Mathematical Biology
Volume67
Issue number4
DOIs
StatePublished - Oct 1 2013
Externally publishedYes

Fingerprint

Immune Response
dynamic models
Therapy
Dynamic models
Dynamic Model
immune response
therapeutics
Statistical Models
Drug Combinations
Reproduction
HIV
Latin Hypercube Sampling
Viruses
Logistic Growth
T-Lymphocytes
Multiple Equilibria
Reproduction number
combination drug therapy
T-cells
Therapeutics

Keywords

  • Antiretroviral therapy
  • Asymptotic stability
  • CD4 T-cells
  • Cytotoxic T lymphocytes
  • HIV

ASJC Scopus subject areas

  • Modeling and Simulation
  • Agricultural and Biological Sciences (miscellaneous)
  • Applied Mathematics

Cite this

Viral dynamics model with CTL immune response incorporating antiretroviral therapy. / Wang, Yan; Zhou, Yicang; Brauer, Fred; Heffernan, Jane M.

In: Journal of Mathematical Biology, Vol. 67, No. 4, 01.10.2013, p. 901-934.

Research output: Contribution to journalArticle

Wang, Yan ; Zhou, Yicang ; Brauer, Fred ; Heffernan, Jane M. / Viral dynamics model with CTL immune response incorporating antiretroviral therapy. In: Journal of Mathematical Biology. 2013 ; Vol. 67, No. 4. pp. 901-934.
@article{e8b93461981f455da3a77d0a6af65a0d,
title = "Viral dynamics model with CTL immune response incorporating antiretroviral therapy",
abstract = "We present two HIV models that include the CTL immune response, antiretroviral therapy and a full logistic growth term for uninfected CD4+ T-cells. The difference between the two models lies in the inclusion or omission of a loss term in the free virus equation. We obtain critical conditions for the existence of one, two or three steady states, and analyze the stability of these steady states. Through numerical simulation we find substantial differences in the reproduction numbers and the behaviour at the infected steady state between the two models, for certain parameter sets. We explore the effect of varying the combination drug efficacy on model behaviour, and the possibility of reconstituting the CTL immune response through antiretroviral therapy. Furthermore, we employ Latin hypercube sampling to investigate the existence of multiple infected equilibria.",
keywords = "Antiretroviral therapy, Asymptotic stability, CD4 T-cells, Cytotoxic T lymphocytes, HIV",
author = "Yan Wang and Yicang Zhou and Fred Brauer and Heffernan, {Jane M.}",
year = "2013",
month = "10",
day = "1",
doi = "10.1007/s00285-012-0580-3",
language = "English (US)",
volume = "67",
pages = "901--934",
journal = "Journal of Mathematical Biology",
issn = "0303-6812",
publisher = "Springer Verlag",
number = "4",

}

TY - JOUR

T1 - Viral dynamics model with CTL immune response incorporating antiretroviral therapy

AU - Wang, Yan

AU - Zhou, Yicang

AU - Brauer, Fred

AU - Heffernan, Jane M.

PY - 2013/10/1

Y1 - 2013/10/1

N2 - We present two HIV models that include the CTL immune response, antiretroviral therapy and a full logistic growth term for uninfected CD4+ T-cells. The difference between the two models lies in the inclusion or omission of a loss term in the free virus equation. We obtain critical conditions for the existence of one, two or three steady states, and analyze the stability of these steady states. Through numerical simulation we find substantial differences in the reproduction numbers and the behaviour at the infected steady state between the two models, for certain parameter sets. We explore the effect of varying the combination drug efficacy on model behaviour, and the possibility of reconstituting the CTL immune response through antiretroviral therapy. Furthermore, we employ Latin hypercube sampling to investigate the existence of multiple infected equilibria.

AB - We present two HIV models that include the CTL immune response, antiretroviral therapy and a full logistic growth term for uninfected CD4+ T-cells. The difference between the two models lies in the inclusion or omission of a loss term in the free virus equation. We obtain critical conditions for the existence of one, two or three steady states, and analyze the stability of these steady states. Through numerical simulation we find substantial differences in the reproduction numbers and the behaviour at the infected steady state between the two models, for certain parameter sets. We explore the effect of varying the combination drug efficacy on model behaviour, and the possibility of reconstituting the CTL immune response through antiretroviral therapy. Furthermore, we employ Latin hypercube sampling to investigate the existence of multiple infected equilibria.

KW - Antiretroviral therapy

KW - Asymptotic stability

KW - CD4 T-cells

KW - Cytotoxic T lymphocytes

KW - HIV

UR - http://www.scopus.com/inward/record.url?scp=84883805706&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84883805706&partnerID=8YFLogxK

U2 - 10.1007/s00285-012-0580-3

DO - 10.1007/s00285-012-0580-3

M3 - Article

VL - 67

SP - 901

EP - 934

JO - Journal of Mathematical Biology

JF - Journal of Mathematical Biology

SN - 0303-6812

IS - 4

ER -