# American Institute of Mathematical Sciences

2015, 12(5): 917-936. doi: 10.3934/mbe.2015.12.917

## Parameters identification for a model of T cell homeostasis

 1 IMB UMR CNRS 5251, Bordeaux University, 3 Place de la Victoire, 33076 Bordeaux Cedex, France, France, France 2 INSERM U897, ISPED, Bordeaux University, Bordeaux, France

Received  November 2014 Revised  April 2015 Published  June 2015

In this study, we consider a model of T cell homeostasis based on the Smith-Martin model. This nonlinear model is structured by age and CD44 expression. First, we establish the mathematical well-posedness of the model system. Next, we prove the theoretical identifiability regarding the up-regulation of CD44, the proliferation time phase and the rate of entry into division, by using the experimental data. Finally, we compare two versions of the Smith-Martin model and we identify which model fits the experimental data best.
Citation: Houssein Ayoub, Bedreddine Ainseba, Michel Langlais, Rodolphe Thiébaut. Parameters identification for a model of T cell homeostasis. Mathematical Biosciences & Engineering, 2015, 12 (5) : 917-936. doi: 10.3934/mbe.2015.12.917
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