Investigations in mathematical modeling and control of the immune system

This thesis investigates the mathematical modeling and control of the human immune system. It sets forth two predator-prey like nonlinear differential equation models (2$\rm\sp{nd}$ order and 11$\rm\sp{th}$ order) that capture the humoral immune response to Haemophilus influenzae type b (Hib) by closely linking the mathematical structure to the underlying physiology, thereby, providing a simulation based test bed for disease evaluation and treatment strategy investigations. Using the second order model, an optimal intravenous antibiotic treatment is found by employing robust optimization control techniques (linear matrix inequality based) to minimize an upper bound on a measure of the total drug delivered. The 11$\rm\sp{th}$ order model builds on recently delineated B-cell physiology incorporating memory B-cells, T-zone and germinal center B-cell dynamics, IgM and IgG antibody concentration profiles, and avidity maturation for primary, secondary, and tertiary Hib bacterial exposures. Partial model validation is demonstrated by exercising the model\u27s robustness in response to changes in the infection dose, the infection strain, level of T-cell stimulation, and the onset-time of the secondary response. The mathematical modeling, controller design, and parameter identification techniques developed herein have broad applicability to illnesses which primarily elicit a humoral immune response. The techniques used in the thesis establish a systematic method for (i) developing complex physiologically based mathematical models of the human immune system, (ii) evaluating drug therapy, determining optimal drug treatments, and evaluating vaccination strategies, and (iii) parameter identification of physical systems plagued by fast and slow modes, widely divergent parameter values, large differences in parameter sensitivities, and a variety of measurement/data problems which include sparse and noisy data