The Effect of a Linear Tuning between the Antigenic Stimulations of CD4+ T Cells and CD4+ Tregs

被引：6
作者：
Yusuf, Aliyu A. [1 ,2 ,3 ]
Figueiredo, Isabel P. [4 ]
Afsar, Atefeh [1 ,2 ]
Burroughs, Nigel J. [5 ]
Pinto, Alberto A. [1 ,2 ]
Oliveira, Bruno M. P. M. [2 ,6 ]
机构：
[1] Univ Porto, Fac Ciencias, Dept Matemat, P-4169007 Porto, Portugal
[2] INESC TEC, LIAAD, P-4200465 Porto, Portugal
[3] Kano Univ Sci & Technol, Dept Math, Kano 3244, Nigeria
[4] Inst Politecn Porto, Inst Super Engn Porto, Dept Matemat, P-4200072 Porto, Portugal
[5] Univ Warwick, Syst Biol Ctr, Coventry CV4 7AL, W Midlands, England
[6] Univ Porto, Fac Ciencias Nutr & Alimentacao, P-4200465 Porto, Portugal
来源：
MATHEMATICS | 2020年 / 8卷 / 02期
关键词：
CD4(+) T cells; CD4(+) Tregs; bifurcation; eigenvalues; ODE model; 58F15; 58F17; 53C35; QUORUM GROWTH THRESHOLDS; IMMUNE-RESPONSE; AUTOIMMUNE-DISEASE; MODEL; SELF; SUPPRESSION; INFECTIONS; ACTIVATION; TOLERANCE; VIRUS;
D O I：
10.3390/math8020293
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We study the equilibria of an Ordinary Differencial Equation (ODE) system where CD4<mml:semantics>+</mml:semantics> effector or helper T cells and Regulatory T cells (Tregs) are present. T cells trigger an immune response in the presence of their specific antigen. Regulatory T cells (Tregs) play a role in limiting auto-immune diseases due to their immune-suppressive ability. Here, we present explicit exact formulas that give the relationship between the concentration of T cells, the concentration of Tregs, and the antigenic stimulation of T cells, when the system is at equilibria, stable or unstable. We found a parameter region of bistability, limited by two thresholds of antigenic stimulation of T cells (hysteresis). Moreover, there are values of the slope parameter of the tuning for which an isola-center bifurcation appears, and, for some other values, there is a transcritical bifurcation. We also present time evolutions of the ODE system.
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页数：14
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