Mathematical model of the primary CD8 T cell immune response: stability analysis of a nonlinear age-structured system.
J Math Biol
; 65(2): 263-91, 2012 Aug.
Article
em En
| MEDLINE
| ID: mdl-21842166
ABSTRACT
The primary CD8 T cell immune response, due to a first encounter with a pathogen, happens in two phases an expansion phase, with a fast increase of T cell count, followed by a contraction phase. This contraction phase is followed by the generation of memory cells. These latter are specific of the antigen and will allow a faster and stronger response when encountering the antigen for the second time. We propose a nonlinear mathematical model describing the T CD8 immune response to a primary infection, based on three nonlinear ordinary differential equations and one nonlinear age-structured partial differential equation, describing the evolution of CD8 T cell count and pathogen amount. We discuss in particular the roles and relevance of feedback controls that regulate the response. First we reduce our system to a system with a nonlinear differential equation with a distributed delay. We study the existence of two steady states, and we analyze the asymptotic stability of these steady states. Second we study the system with a discrete delay, and analyze global asymptotic stability of steady states. Finally, we show some simulations that we can obtain from the model and confront them to experimental data.
Texto completo:
1
Coleções:
01-internacional
Base de dados:
MEDLINE
Assunto principal:
Dinâmica não Linear
/
Modelos Imunológicos
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Linfócitos T CD8-Positivos
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Coriomeningite Linfocítica
Limite:
Animals
Idioma:
En
Ano de publicação:
2012
Tipo de documento:
Article