| Biological systems are inherently complex networks with many unknown components. Many different techniques have been used to increase the general understanding of these systems. The method outlined in this dissertation uses data collected from test subjects that were exposed to various pathogens to create predictive models of the immune response, which are then used to design an intervention program to return the subject to a healthy state. Previous methods used to construct models of biological systems originate from a preconceived notion of the way that the system evolves. The modeling approach based solely on data gives a more general method that does not rely on underlying assumptions of the interactions of the system, and instead only uses collected data to approximate the dynamics inherent in the system.;In the past, the creation of new treatments for various diseases have taken numerous laboratory trials to hone in on the best drug and dosage combinations. The use of mathematical tools can eliminate significant amounts of this guesswork. A new method of studying optimal treatment plans for a given pathogen implements control techniques. Numerical optimization problems are formulated to attempt to recover a combination of proteins to administer along with standard optimal control methods to determine a dosage schedule. The determination of the plan has many customizable qualities that can be chosen by the implementor, such as the creation of penalties for unwanted outcomes in the treatment plan and restrictions on which biological markers can be considered for the synthesis of the treatment. The results are given in a medically translatable view, which also can contribute to the understanding of the importance of specific biomarkers that may not have been noticed without these numerical methods. |
