Alexander, H.K. and Wahl, L.M. (2010) Self-Tolerance and Autoimmunity in a Regulatory T Cell Model. Bulletin of Mathematical Biology, 73, 33-71.
https://doi.org/10.1007/s11538-010-9519-2

has been cited by the following article:

• TITLE: A Type of Hopf Bifurcation in Models with Holling-II Type Multiple Sclerosis

  AUTHORS: Manhui He

  KEYWORDS: Multiple Sclerosis Model, Holling-II Type Functional Response, Equilibrium Point, Stability, Hopf Bifurcation

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.13 No.1, January 26, 2025

  ABSTRACT: Multiple autoimmune diseases often exhibit a cyclic pattern of relapse and remission, with significant periods of loss of self-tolerance being interrupted by recurrent autoimmune events. In this article, we explore a specific type of terminally differentiated regulatory T cell HLA−D R + T Reg cells, and their application in existing autoimmune disease models. We also conduct an in-depth study on a multiple sclerosis model. This model incorporates a Holling-II type functional response mechanism. The focus of the study is to analyze whether the equilibrium points of the system have local asymptotic stability and determine the conditions for the existence of Hopf bifurcation. Furthermore, the direction of Hopf bifurcations and the stability of its periodic solutions can be analyzed through normal form theory and center manifold theorem.