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

Hongjing Shi; Wanbiao Ma

doi:10.3934/mbe.2006.3.237

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2006, Volume 3, Issue 1: 237-248. Doi: 10.3934/mbe.2006.3.237

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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
2.
Department of Applied Mathematics, School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083

Received: January 31, 2005

Revised: April 30, 2005

Published: October 2005

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Abstract

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.

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Mathematics Subject Classification: 92D30, Secondary 92D25,34K20.

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