Approximate equilibria for a T cell and treg model

• Type: Article in International Scientific Journal
• Date: 2015

Authors

Oliveira, BMPM (Author) FCNAUP; Figueiredo, IP (Author) Other; Burroughs, NJ (Author) Other; Alberto A. Pinto (Author) FCUP

Journal

Title: Applied Mathematics and Information Sciences

Vol. 9

Pages: 2221-2231

ISSN: 1935-0090

Publisher: Natural Sciences Publishing

Indexing

ISI Web of Knowledge

Scopus - 4 Citations

Other information

Authenticus ID: P-00G-EJ0

DOI: 10.12785/amis/090502

Abstract (EN): 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. © 2015 NSP Natural Sciences Publishing Cor.

Language: English

Type (Professor's evaluation): Scientific