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

Aliyu A. Yusuf, Isabel P. Figueiredo, Atefeh Afsar, Nigel J. Burroughs, Alberto A. Pinto and Bruno M. P. M. Oliveira
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Aliyu A. Yusuf: Departamento de Matemática, Faculdade de Ciências, Universidade do Porto, 4169-007 Porto, Portugal
Isabel P. Figueiredo: Departamento de Matemática, Instituto Superior de Engenharia do Porto, Instituto Politécnico do Porto, 4200-072 Porto, Portugal
Atefeh Afsar: Departamento de Matemática, Faculdade de Ciências, Universidade do Porto, 4169-007 Porto, Portugal
Nigel J. Burroughs: Systems Biology Centre, University of Warwick, Coventry CV4 7AL, UK
Alberto A. Pinto: Departamento de Matemática, Faculdade de Ciências, Universidade do Porto, 4169-007 Porto, Portugal
Bruno M. P. M. Oliveira: Laboratório de Inteligência Artificial e Apoio à Decisão (LIAAD)–Instituto de Engenharia de Sistemas e Computadores, Tecnologia e Ciência (INESC TEC), 4200-465 Porto, Portugal

Mathematics, 2020, vol. 8, issue 2, 1-14

Abstract: 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.

Keywords: CD4 + T cells; CD4 + Tregs; bifurcation; eigenvalues; ODE model (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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