Global asymptotic stability of a nonlinear time-delayed system of cells in the thymus

Shi, Hongjing; Ma, Wanbiao; Duan, Zhisheng

doi:10.1016/j.na.2009.01.143

Cited by 2 publications

(6 citation statements)

References 6 publications

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“…These conditions are very similar to those in (7) and provides constraints on the rates describing the evolution of M 4 and M 8 populations. These constraints will be used in the following section in order to estimate values for the rates which ensures that the stationary states of all populations are asymptotically stable.…”

Section: Casementioning

confidence: 54%

“…The direct computation of the stationary solutions of the system (1) is difficult, mainly because of the presence of the joint term Z corresponding to the total number of cells in all populations. The solution proposed in [3] and [7] to simplify this computation is to consider the ratio Z/K negligeable. This approximation is valid in the early stage of the evolution when the number of cells in each population is very small, but it is no more valid as the populations approach the stationary state.…”

Section: Stability Analysismentioning

confidence: 99%

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Stability Analysis and its Impact on the Parameters Estimation for a Logistic Growth Model

Moatar-Moleriu¹

2013

Annals of West University of Timisoara - Mathematics

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This paper presents a stability analysis of a system of differential equations describing the evolution of T-cells populations. The analyzed system corresponds to a well-known four-compartmental model of the thymus which involves a logistic growth term. Unlike existing results on stability for this model which focus either only on the global population or on the two dominant double-positive and double-negative populations, the results presented in this paper provide sufficient conditions for asymptotic stability of all four populations, taken separately. The derived conditions involve parameters related to cells proliferation, death and transfer rates and are used as constraints in the least-square optimization procedure which provides estimates for all parameters of the model. The usage of the constraints derived from the stability analysis ensures that the estimated parameters lead to a mathematical model with an asymptotically stable fixed point.

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Section: Casementioning

confidence: 54%

Section: Stability Analysismentioning

confidence: 99%

Stability Analysis and its Impact on the Parameters Estimation for a Logistic Growth Model

Moatar-Moleriu¹

2013

Annals of West University of Timisoara - Mathematics

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“…Let W = W 1 < 0 be another equilibrium of the system (9). It has the following results in [27,28]. Lemma 3.2.…”

Section: Global Stability Of the Equilibriummentioning

confidence: 99%

“…Next, motivated by the methods in [1], [4], [16][17][18], [28], [31][32][33], and [35], let us define a series of differentiable functionals V i (i = 2, 3, 4, 5, 6, 7), and then consider their derivatives along the solutions of the system (9), for t ≥ t 2 + σ,…”

Section: Global Stability Of the Equilibriummentioning

confidence: 99%

“…In [10], by using stability theory of ordinary differential equations, detailed theoretical analysis of global asymptotic stability of the positive equilibrium of the model (1) has been given. Then, based on some important experimental date, in [27,28], time delays are introduced into the model (1) and global dynamic properties of the positive equilibrium of the system has been analyzed by constructing suitable Liapunov functionals.…”

Section: Introductionmentioning

confidence: 99%

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Global stability analysis of the equilibrium of an improved time-delayed dynamic model to describe the development of T cells in the thymus

Xiao

et al. 2017

Filomat

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In this paper, based on some biological meaning, triple-negative T cells (TN) and the immature single-positive T cells (CD3 − 4 + 8 − and CD3 − 4 − 8 +) have been introduced into well known Mehr's nonlinear dynamic model which is used to describe proliferation, differentiation and death of T cells in the thymus (Modeling positive and negative selection and differentiation processes in the thymus, Journal of Theoretical Biology, 175 (1995) 103-126), and a class of improved nonlinear dynamic model with seven state variables and time delays has been proposed. Then, by using quasi-steady-state approximation and some classical analysis techniques of functional differential equations, the local and global stability of the equilibrium of the model have been analysed. Finally, some numerical simulations are given to summarize the applications of the theoretical results.

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Global asymptotic stability of a nonlinear time-delayed system of cells in the thymus

Cited by 2 publications

References 6 publications

Stability Analysis and its Impact on the Parameters Estimation for a Logistic Growth Model

Stability Analysis and its Impact on the Parameters Estimation for a Logistic Growth Model

Global stability analysis of the equilibrium of an improved time-delayed dynamic model to describe the development of T cells in the thymus

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