A delay-dependent model with HIV drug resistance during therapy

Yan Wang, Fred Brauer, Jianhong Wu, Jane M. Heffernan

Research output: Contribution to journalArticle

15 Citations (Scopus)

Abstract

The use of combination antiretroviral therapy has proven remarkably effective in controlling HIV disease progression and prolonging survival. However, the emergence of drug resistance can occur. It is necessary that we gain a greater understanding of the evolution of drug resistance. Here, we consider an HIV viral dynamical model with general form of target cell density, drug resistance and intracellular delay incorporating antiretroviral therapy. The model includes two strains: wild-type and drug-resistant. The basic reproductive ratio for each strain is obtained for the existence of steady states. Qualitative analysis of the model such as the well-posedness of the solutions and the equilibrium stability is provided. Global asymptotic stability of the disease-free and drug-resistant steady states is shown by constructing Lyapunov functions. Furthermore, sufficient conditions related to the properties of the target cell density are obtained for the local asymptotic stability of the positive steady state. Numerical simulations are conducted to study the impact of target cell density and intracellular delay focusing on the stability of the positive steady state. The occurrence of Hopf bifurcation of periodic solutions is shown to depend on the target cell density.

Original languageEnglish (US)
Pages (from-to)514-531
Number of pages18
JournalJournal of Mathematical Analysis and Applications
Volume414
Issue number2
DOIs
StatePublished - Jun 15 2014
Externally publishedYes

Fingerprint

Drug Resistance
Delay-dependent
Therapy
Asymptotic stability
Target
Cell
Drugs
Hopf bifurcation
Lyapunov functions
Local Asymptotic Stability
Global Asymptotic Stability
Dynamical Model
Qualitative Analysis
Progression
Well-posedness
Model
Hopf Bifurcation
Lyapunov Function
Periodic Solution
Computer simulation

Keywords

  • Antiretroviral therapy
  • Asymptotic stability
  • Drug resistance
  • HIV
  • Hopf bifurcation
  • Intracellular delay

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Cite this

A delay-dependent model with HIV drug resistance during therapy. / Wang, Yan; Brauer, Fred; Wu, Jianhong; Heffernan, Jane M.

In: Journal of Mathematical Analysis and Applications, Vol. 414, No. 2, 15.06.2014, p. 514-531.

Research output: Contribution to journalArticle

Wang, Yan ; Brauer, Fred ; Wu, Jianhong ; Heffernan, Jane M. / A delay-dependent model with HIV drug resistance during therapy. In: Journal of Mathematical Analysis and Applications. 2014 ; Vol. 414, No. 2. pp. 514-531.
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