Mathematical Modeling for Homogeneous Tumor with Delay in Time

Due to the properties of tumor cell, the tumor establishes itself in the organ and grows there, so there is a competition between the tumor cells and host cell (normal cells) for nutrients. Evidences show that high dietary phosphorus increases the rate of protein synthesis and thus the cell number. So, other than oxygen, sulfur, the important element that both tumor cells and normal cells need is phosphorus. Hence, the proliferation and growth rate of both tumor cells and healthy cells depends on the content of phosphorus available to them. So, the mathematical model with time delay is prepared in which the growth rate of tumor cells and normal cells are function of phosphorus with their restrictions. And by applying suitable implications on the model and studying the simulations we will come to know its effects on tumor growth.

Keywords:

Tumor , Mathematical Modeling , Phosphorus , Extra Cellular Phosphorus , Homogeneous Tumor , Micro Vessels , Angiogenesis , Delay Differential Equations