Modelling, dynamics and games

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

Publication . Yusuf, Aliyu; Figueiredo, Isabel; Afsar, Atefeh; Burroughs, Nigel; Pinto, Alberto; Oliveira, Bruno

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.

2020Artigo científico

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Entidade financiadora

Fundação para a Ciência e a Tecnologia

Programa de financiamento

3599-PPCDT

Número da atribuição

PTDC/MAT-APL/31753/2017