This paper presents a four-unit, four-component mathematical model of iodine metabolism and its impact on thyroid hormone levels in the body. We focus on the relationships between iodine (I-), triiodothyronine (T3), thyroxine (T4), and thyroid-stimulating hormone (TSH) through the mixer, thyroid, sensor (pituitary gland), and metabolism. Iodine plays a fundamental role in maintaining metabolic homeostasis, as it is essential for the synthesis of T3 and T4, which regulate weight, energy, and other physiological functions. Iodine deficiency, which is one of the most common nutrient deficiencies in the world, can lead to hypothyroidism, a condition characterized by fatigue, weight gain, and cognitive impairments [1]. Our model tracks the movement of iodine through dietary intake, thyroid absorption, hormone synthesis, feedback regulation via TSH, and deiodization in metabolism. By evaluating different forms of the accounting equation governing these processes, we have concluded three key results. 1) Iodide availability directly impacts levels of T3 and T4 production, with both component flow rates declining at day 70 in a mildly diseased state, and day 60 in a severely diseased state. 2) TSH is an early diagnostic indicator of thyroid issues, with TSH levels rising to magnitudes of 25x in just ten days, nearly six times quicker than other biological indicators. 3) There is a 5 day difference in iodine storage depletion between mild and severe iodide deficiency. Understanding these results quantitatively provides insights into thyroid disorders and informs strategies for managing iodine deficiency on both individual and public health levels.

46 pages, 8 figures,