Mathematical model of the primary CD8 T cell immune response: stability analysis of a nonlinear age-structured system. - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Journal of Mathematical Biology Année : 2012

Mathematical model of the primary CD8 T cell immune response: stability analysis of a nonlinear age-structured system.

Résumé

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.

Dates et versions

hal-00649219 , version 1 (07-12-2011)

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Emmanuelle Terry, Jacqueline Marvel, Christophe Arpin, Olivier Gandrillon, Fabien Crauste. Mathematical model of the primary CD8 T cell immune response: stability analysis of a nonlinear age-structured system.. Journal of Mathematical Biology, 2012, 65, pp.263-291. ⟨10.1007/s00285-011-0459-8⟩. ⟨hal-00649219⟩
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