Back to Search
Start Over
Mathematical model of the primary CD8 T cell immune response: stability analysis of a nonlinear age-structured system.
- Source :
- Journal of Mathematical Biology; Aug2012, Vol. 65 Issue 2, p263-291, 29p
- Publication Year :
- 2012
-
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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 03036812
- Volume :
- 65
- Issue :
- 2
- Database :
- Complementary Index
- Journal :
- Journal of Mathematical Biology
- Publication Type :
- Academic Journal
- Accession number :
- 77495327
- Full Text :
- https://doi.org/10.1007/s00285-011-0459-8