TITLE:
Dynamics of a Class of Multiple Sclerosis Models with Saturated Activation Rates of T Cells
AUTHORS:
Yu Su
KEYWORDS:
Multiple Sclerosis Model, Saturated Functional Response, Equilibrium Point, Stability, Hopf Bifurcation
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.13 No.2,
February
25,
2025
ABSTRACT: Many autoimmune diseases exhibit an alternating pattern of relapses and remissions in which the apparent self-tolerance phase is interrupted by periodic autoimmune episodes. In this paper, we introduce a class of terminally differentiated effector T cells to an existing model of autoimmune disease and investigate the stability and Hopf branching phenomenon in a model of multiple sclerosis with a saturable functional response. First, we explore the local asymptotic stability of the equilibrium point and propose conditions for the existence of Hopf branching. Finally, with the help of canonical type theory and the central manifold theorem, we analyze the direction of Hopf branching and the stability of branching periodic solutions.