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

Abstract

Based on some important experimental dates, in this paper weshall introduce time delays into Mehrs's non-linear differential system modelwhich is used to describe proliferation, differentiation and death of T cells inthe thymus (see, for example, [3], [6], [7] and [9]) and give a revised nonlineardifferential system model with time delays. By using some classical analysistechniques of functional differential equations, we also consider local and globalasymptotic stability of the equilibrium and the permanence of the model.

Keywords

• time delay
• transcendental equation
• t cells
• permanence.
• stability
• quasi-steady-state approximation