Neonatal jaundice (icterus neonatorium) is caused by the excessive accumulation of bilirubin, a byproduct of the red blood cells decomposition. Shortly after birth, newborn babies carry a very high level of red blood cells and thus a high concentration of bilirubin. If a baby’s liver is premature, it cannot process the bilirubin as quickly as its body produces. The excessive bilirubin then flows out of the bloodstream and permeates to the body surface causing yellow-colored skin and sclera of the eye and inside lining of the mouth. If jaundice is left untreated, the infant can develop Kernicterus, a form of permanent brain damage. In this paper, we derive a mathematical model for the mass transport of the bilirubin concentration in the human body using the Mass Balance Law. We also incorporate into the model three types of treatments: blood transfusion, phototherapy, and medication. Our goal is, by observing the bilirubin concentration in the blood, to find the optimal treatment(s) to bring the concentration of bilirubin down to a normal level. We will also develop a program that automatically chooses the treatments based on the severity of the bilirubin level.