American Institute of Mathematical Sciences

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2006, 3(1): 237-248. doi: 10.3934/mbe.2006.3.237

An improved model of t cell development in the thymus and its stability analysis

Hongjing Shi 1, and  Wanbiao Ma 2,

1. 

Department of Mathematics and Mechanics, Applied Science College, University of Science and Technology Beijing, Beijing 100083, China
2. 

Department of Applied Mathematics, School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083

Received  February 2005 Revised  May 2005 Published  November 2005

Based on some important experimental dates, in this paper we shall introduce time delays into Mehrs's non-linear differential system model which is used to describe proliferation, differentiation and death of T cells in the thymus (see, for example, [3], [6], [7] and [9]) and give a revised nonlinear differential system model with time delays. By using some classical analysis techniques of functional differential equations, we also consider local and global asymptotic stability of the equilibrium and the permanence of the model.
Keywords: time delay, transcendental equation, T cells, permanence., stability, quasi-steady-state approximation.
Mathematics Subject Classification: 92D30, Secondary 92D25,34K2.
Citation: Hongjing Shi, Wanbiao Ma. An improved model of t cell development in the thymus and its stability analysis. Mathematical Biosciences & Engineering, 2006, 3 (1) : 237-248. doi: 10.3934/mbe.2006.3.237
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