Mathematical Biosciences and Engineering (MBE)

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

Pages: 237 - 248, Volume 3, Issue 1, January 2006      doi:10.3934/mbe.2006.3.237

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Hongjing Shi - Department of Mathematics and Mechanics, Applied Science College, University of Science and Technology Beijing, Beijing 100083, China (email)
Wanbiao Ma - Department of Applied Mathematics, School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China (email)

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.

Keywords:  T cells, quasi-steady-state approximation, time delay, transcendental equation, stability, permanence.
Mathematics Subject Classification:  92D30, Secondary 92D25,34K20.

Received: February 2005;      Accepted: May 2005;      Available Online: November 2005.