Approximate Equilibria for a T Cell and Treg Model

Authors

Bruno M. P. M. Oliveira, Faculdade de Ciˆencias da Nutric¸ ?ao e Alimentac¸ ?ao da Universidade do Porto, R. Dr. Roberto Frias, 4250-465 Porto, Portugal.\\ LIAAD - INESC Tec Porto, R. Dr. Roberto Frias, 4250-465 Porto, Portugal.Follow
Isabel P. Figueiredo, Instituto Superior de Engenharia do Porto, R. Dr. Ant´onio Bernardino de Almeida, 431, 4200-072 Porto, Portugal.\\ LIAAD - INESC Tec Porto, R. Dr. Roberto Frias, 4250-465 Porto, Portugal.Follow
Nigel J. Burroughs, Mathematics Institute and Warwick Systems Biology Centre, University of Warwick, Coventry. CV4 7AL. UK.Follow
Alberto A. Pinto, Departamento de Matem´atica, Faculdade de Ciˆencias da Universidade do Porto, R. do Campo Alegre 687, 4169-007 Porto, Portugal.\\ LIAAD - INESC Tec Porto, R. Dr. Roberto Frias, 4250-465 Porto, Portugal.Follow

Author Country (or Countries)

Portugal.

Abstract

We analyse a model of immune response by T cells (CD4), where regulatory T cells (Tregs) act by inhibiting IL-2 secretion. We introduced an asymmetry reflecting that the difference between the growth and death rates can be higher for the active T cells and the active Tregs than for the inactive T cells and inactive Tregs. This asymmetry mimics the presence of memory T cells. In this paper we start by analysing the model in the absence of Tregs. We obtain an explicit formula that gives approximately the antigenic stimulation of T cells from the concentration of Tregs. Afterwards, we present an explicit formula that describes approximately the balance between the concentration of T cells and the concentration of Tregs; and an explicit formula that relates approximately the antigenic stimulation of T cells, the concentration of T cells and the concentration of Tregs. For our parameter values, the relation between the antigenic stimulation of T cells and the concentration of T cells is an hysteresis that is unfold when some of the parameters are changed. We also consider a linear tuning between the antigenic stimulation of T cells and the antigenic stimulation of Tregs. Again, we have obtained an explicit formula relating approximately the antigenic stimulation of T cells, the concentration of T cells and the concentration of Tregs. With it, we can explain the appearance of an isola and a transcritical bifurcation.

Recommended Citation

M. P. M. Oliveira, Bruno; P. Figueiredo, Isabel; J. Burroughs, Nigel; and A. Pinto, Alberto (2023) "Approximate Equilibria for a T Cell and Treg Model," Applied Mathematics & Information Sciences: Vol. 09: Iss. 5, Article 2.
Available at: https://digitalcommons.aaru.edu.jo/amis/vol09/iss5/2