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The effect of a linear tuning between the antigenic stimulations of CD4+ t cells and CD4+ tregs

Mathematics, ISSN: 2227-7390, Vol: 8, Issue: 2
2020
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Article Description

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.

Bibliographic Details

Aliyu A. Yusuf; Atefeh Afsar; Alberto A. Pinto; Bruno M.P.M. Oliveira; Isabel P. Figueiredo; Nigel J. Burroughs

MDPI AG

Computer Science; Mathematics; Engineering

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