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Abstract
Mathematical modeling is the process of quantitatively describing a particular system, process, or phenomenon. It can be utilized to detect patterns and interactions that cannot be understood with the current data available and to test hypotheses that are difficult to evaluate experimentally. In this dissertation, mathematical modeling is used in three unique ways. (1) We extended an existing mathematical model of glucose and insulin dynamics to account for renal filtration and excretion of glucose, in order to investigate the effect of treatment for a diabetes medication. We quantified and compared daily glucose and sodium reabsorption through sodium glucose cotransporters 2 (SGLT2) in healthy, controlled, and uncontrolled diabetes and following treatment with an SGLT2 inhibitor. (2) We captured high frequency physiological data (e.g. temperature, blood pressure) via telemetry from nonhuman primates during health and malaria infection. Using a multiple-component cosinor model, we were able to quantify changes in biological rhythm parameters that helped classify between health and disease states. (3) We created a model of erythrocytic glucose to investigate the role of malaria parasite glucose utilization on red blood cell bursting cycles. The malaria parasite cannot store energy and relies on the host's erythrocytic glucose. Infected erythrocytes burst at regular 24, 48, or 72 hr intervals. The model was applied to understand and propose experimentally testable hypotheses regarding the role of malaria parasites in altering cell energy availability and triggering bursting. Overall, mathematical modeling in these research areas provided novel insights into the various health and disease states.