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Mathematical Biosciences and Engineering

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

  • 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: 01 February 2005 Accepted: 29 June 2018 Published: 01 November 2005

  • MSC : 92D30, Secondary 92D25,34K20.

  • 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.

    Citation: Hongjing Shi, Wanbiao Ma. An improved model of t cell development in the thymus and its stability analysis[J]. Mathematical Biosciences and Engineering, 2006, 3(1): 237-248. doi: 10.3934/mbe.2006.3.237

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  • 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.


  • This article has been cited by:

    1. Hongjing Shi, Wanbiao Ma, Zhisheng Duan, Global asymptotic stability of a nonlinear time-delayed system of cells in the thymus, 2009, 71, 0362546X, 2699, 10.1016/j.na.2009.01.143
    2. Anna Q. Cai, Kerry A. Landman, Barry D. Hughes, Colleen M. Witt, T cell development in the thymus: From periodic seeding to constant output, 2007, 249, 00225193, 384, 10.1016/j.jtbi.2007.07.028
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  • © 2006 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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