Mathematical modelling of cytokine-mediated CD4+ T cell dynamics in autoimmunity

Abstract

The primary function of the human immune system is the protection of the host from invasion by virus, bacteria, or parasites. The mechanism of immune system is to discriminate between cells infected with a pathogen such as virus and the uninfected cells of the host. The failure of this mechanism can lead to a pathological immune response known as autoimmune disease, where specific cells or organs are attacked by the immune system. This thesis presents a comprehensive exploration of the cytokinemediated dynamics of CD4+ T cells during immune responses to uveitis, a complex ocular inflammatory disease. I propose a novel mathematical model that characterises the interactions between immune cells, cytokines, and host cells during uveitis. The model reveals two distinct steady states, one representing host cell death and the other a chronic inflammation state with all components active. The impact of key parameters, such as the rate of host cell destruction by cytotoxic CD4+ T cells, is examined. Importantly, further investigations unveil the role of regulatory CD4+ T cells in preventing autoimmune responses and offers insights into the conditions favouring chronic inflammation versus autoimmunity. I investigate the influence of stochasticity on uveitis dynamics. The methodology of continuous-time Markov chains is applied to derive a master equation, and van Kampen’s expansions lead to a linear Fokker-Planck equation. Stochastic differential equation models are developed and analysed to explore the role of randomness in immune response outcomes. The chapter provides critical insights into how stochasticity affects the system’s behaviour, fluctuations around steady states, and potential future applications. I explore the impact of time delays in immune response dynamics. A time-delayed model is developed, accounting for delays associated with CD4+ T cell proliferation and interleukin IL-2 stimulation. The chapter unveils parameter regimes where the system prevents autoimmune responses through the regulation of regulatory CD4+ T cells and the cytokine IL-2. The role of IL-2 in maintaining chronic inflammation is examined, highlighting the sensitivity of immune responses to time-delayed processes.