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

• Main Author: Yusuf, Aliyu
• Publication Date: 2020
• Other Authors: Figueiredo, Isabel, Afsar, Atefeh, Burroughs, Nigel, Pinto, Alberto, Oliveira, Bruno
• Format: Article
• Language: eng
• Source: Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
• Download full: http://hdl.handle.net/10400.22/19470
• topic: CD4+ T cells; CD4+ Tregs; Bifurcation; Eigenvalues; ODE model

We study the equilibria of an Ordinary Differencial Equation (ODE) system where CD4 + 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.