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Yusuf, AA; Figueiredo, IP; Afsar, A; Burroughs, NJ; Pinto, AA; Oliveira, BMPM (2020) The Effect of a Linear Tuning between the Antigenic Stimulations of CD4(+) T Cells and CD4(+) Tregs. Mathematics 8 293

Yusuf, AA; Figueiredo, IP; Afsar, A; Burroughs, NJ; Pinto, AA; Oliveira, BMPM (2020) The Effect of a Linear Tuning between the Antigenic Stimulations of CD4(+) T Cells and CD4(+) Tregs. Mathematics 8 293

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.

Thu 02 Apr 2020, 11:37