A Mathematical Model of Calcium Homeostasis with Time Delay

摘要

Calcium in its ionized form is needed in the adequate amount so that all cells in human body will function properly. Parathyroid hormone and vitamin D are two major hormones that participate in the control of calcium homeostasis. Here, we develop a mathematical model to study the change in the serum level of calcium ion due to the change in the serum levels of parathyroid hormone and vitamin D. However, the effects of parathyroid hormone and vitamin D on the change of the serum level of calcium ion do not occur immediately, time delay is also observed clinically. Hence, the time delay is also incorporated in our model. Hopf bifurcation theorem is then utilized so that we obtain the conditions on the model parameters for which a periodic solution can be assured.