Bifurcations and multi-stability in a model of cytokine-mediated autoimmunity

TL;DR

This paper models immune response dynamics, focusing on cytokines and T cells, revealing how different parameters lead to normal, chronic, or autoimmune states, with initial conditions influencing outcomes.

Contribution

It introduces a mathematical model capturing bifurcations and multi-stability in cytokine-mediated autoimmunity, highlighting the role of Tregs and activation thresholds.

Findings

Parameter regions correspond to different immune regimes

Bifurcation analysis identifies stability boundaries

Initial conditions influence immune response outcomes

Abstract

This paper investigates the dynamics of immune response and autoimmunity with particular emphasis on the role of regulatory T cells (Tregs), T cells with different activation thresholds, and cytokines in mediating T cell activity. Analysis of the steady states yields parameter regions corresponding to regimes of normal clearance of viral infection, chronic infection, or autoimmune behaviour, and the boundaries of stability and bifurcations of relevant steady states are found in terms of system parameters. Numerical simulations are performed to illustrate different dynamical scenarios, and to identify basins of attraction of different steady states and periodic solutions, highlighting the important role played by the initial conditions in determining the outcome of immune interactions.