A Study of the Synergies Between Control Mechanisms in the Immune System and the Variable Structure Control Paradigm

This thesis argues that variable structure control theory finds application in immunology. The immune system maintains a healthy state by using feedback to switch on and off immune responses. Experimental and mathematical work has analysed the dynamics of the immune response of T cells, relatively little attention has been paid to examine the underlying control paradigm. Besides, in modelling and simulation studies, it is necessary to evaluate the impact of uncertainty and perturbations on immunological dynamics. This is important to deliver robust predictions and insights. These facts motivate considering variable structure control techniques to investigate the control strategy and robustness of the immune system in the context of immunity to infection and tolerance. The results indicate that the dynamic response of T cells following foreign or self-antigen stimulation behaves as a naturally occurring switched control law. Further, the reachability analysis from sliding mode control highlights dynamical conditions to assess the performance and robustness of the T cell response dynamics. Additionally, this approach delivers dynamical conditions for the containment of Human Immunodeficiency Virus (HIV) infection by the HIV-specific CD8+ T cell response and antiretroviral therapy by enforcing a sliding mode on a manifold associated with the infection-free steady-state. This condition for immunity reveals particular patterns for early diagnosis of eventual success, marginal and failure cases of antiretroviral therapy. Together, the findings in this thesis evidence that variable structure control theory presents a useful framework to study health and disease dynamics as well as to monitor the performance of treatment regimes.