Mathematical Biosciences and Engineering, 2006, 3(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

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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Keywords time delay; transcendental equation; T cells; permanence.; stability; quasi-steady-state approximation

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


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, Nonlinear Analysis: Theory, Methods & Applications, 2009, 71, 7-8, 2699, 10.1016/
  • 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, Journal of Theoretical Biology, 2007, 249, 2, 384, 10.1016/j.jtbi.2007.07.028

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