title: Mathematical model of the primary CD8 T cell immune response: stability analysis of a nonlinear age-structured system.
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.
authors.affiliation: Université de Lyon, Université Lyon 1, CNRS UMR 5208, Institut Camille Jordan, 43 blvd du 11 novembre 1918, 69622, Villeurbanne-Cedex, France. terry@math.univ-lyon1.fr
authors.forename: Emmanuelle
authors.initials: E
authors.lastname: Terry
authors.forename: Jacqueline
authors.initials: J
authors.lastname: Marvel
authors.forename: Christophe
authors.initials: C
authors.lastname: Arpin
authors.forename: Olivier
authors.initials: O
authors.lastname: Gandrillon
authors.forename: Fabien
authors.initials: F
authors.lastname: Crauste
mesh_terms: D000818:Animals; D018414:CD8-Positive T-Lymphocytes / Q000276:immunology*; D003198:Computer Simulation; D007156:Immunologic Memory; D008213:Lymphocyte Activation / Q000276:immunology; D008216:Lymphocytic Choriomeningitis / Q000276:immunology*; D051379:Mice; D018448:Models, Immunological; D017711:Nonlinear Dynamics