An age-structured model for T cell homeostasis in vivo

Bedr'Eddine Ainseba, Houssein Ayoub, Michel Langlais

Research output: Contribution to journalArticle

Abstract

In this study, we consider a model of T cell proliferation in vivo which is structured by age and CD44 expression. This model is rewritten as an age-structured model system without the CD44 structure, and we investigate its asymptotic behavior. We find that there exists one or three stationary solutions when cells undergo at least five divisions and only one stationary solution when cells undergo at most three divisions. The limiting case with four divisions is numerically handled. By applying the Lyapunov method, we prove that the stationary solution is globally asymptotically stable in some regions of parameter space.

Original languageEnglish
Pages (from-to)1463-1485
Number of pages23
JournalSIAM Journal on Applied Mathematics
Volume74
Issue number5
DOIs
Publication statusPublished - 1 Jan 2014
Externally publishedYes

Fingerprint

Age-structured Model
Homeostasis
T-cells
Stationary Solutions
Division
Lyapunov methods
Lyapunov Methods
Cell Proliferation
Globally Asymptotically Stable
Cell
Cell proliferation
Parameter Space
Limiting
Asymptotic Behavior
Model

Keywords

  • Global asymptotic stability
  • Nonlinear dynamical systems
  • Structured populations
  • T cell homeostasis

ASJC Scopus subject areas

  • Applied Mathematics

Cite this

An age-structured model for T cell homeostasis in vivo. / Ainseba, Bedr'Eddine; Ayoub, Houssein; Langlais, Michel.

In: SIAM Journal on Applied Mathematics, Vol. 74, No. 5, 01.01.2014, p. 1463-1485.

Research output: Contribution to journalArticle

Ainseba, Bedr'Eddine ; Ayoub, Houssein ; Langlais, Michel. / An age-structured model for T cell homeostasis in vivo. In: SIAM Journal on Applied Mathematics. 2014 ; Vol. 74, No. 5. pp. 1463-1485.
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