Dynamics of Immunological Models

Authors: A A Pinto N J Burroughs M Ferreira B M P M Oliveira

Publish Date: 2010/08/04

Volume: 58, Issue: 4, Pages: 391-404

PDF Link

Abstract

We analyse the effect of the regulatory T cells Tregs in the local control of the immune responses by T cells We obtain an explicit formula for the level of antigenic stimulation of T cells as a function of the concentration of T cells and the parameters of the model The relation between the concentration of the T cells and the antigenic stimulation of T cells is an hysteresis that is unfold for some parameter values We study the appearance of autoimmunity from crossreactivity between a pathogen and a self antigen or from bystander proliferation We also study an asymmetry in the death rates With this asymmetry we show that the antigenic stimulation of the Tregs is able to control locally the population size of Tregs Other effects of this asymmetry are a faster immune response and an improvement in the simulations of the bystander proliferation The rate of variation of the levels of antigenic stimulation determines if the outcome is an immune response or if Tregs are able to maintain control due to the presence of a transcritical bifurcation for some tuning between the antigenic stimuli of T cells and Tregs This behavior is explained by the presence of a transcritical bifurcationWe thank LIAADINESC Porto LA Calouste Gulbenkian Foundation PRODYNESF POCTI and POSI by FCT and Ministério da Ciência e da Tecnologia and the FCT Pluriannual Funding Program of the LIAADINESC Porto LA and of the Research Center of Mathematics of University of Minho for their financial support M Ferreira also acknowledges the financial support from the FCT grant with reference SFRH/BD/27706/2006 Part of this research was developed during a visit by the authors to the CUNY IHES IMPA MSRI SUNY Isaac Newton Institute University of Berkeley and University of Warwick We thank them for their hospitality

Keywords: