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

• Main Author: Yusuf, AA
• Publication Date: 2020
• Other Authors: Figueiredo, IP, Afsar, A, Burroughs, NJ, Pinto, A.A., Bruno M P M Oliveira
• Format: Article
• Language: eng
• Source: Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
• Download full: https://hdl.handle.net/10216/126870
• topic: Ciências da Saúde, Ciências médicas e da saúde; Health sciences, Medical and Health sciences

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.