Journal article Open Access

Mathematical Modelling of the Dynamics of Tumor Growth and its Optimal Control

Jannatun Irana Ira; Md. Shahidul Islam; J C Misra; Md. Kamrujjaman

Abstract: In the last few decades, the dynamics of tumor cells and their growths are presented via clinical, experimental, and theoretical approaches, which leads to the development of the new idea of multiple cancer therapies to control and reduce the death rate for earlier detection. In this paper, we discussed the dynamics of tumor cell growth and its treatment process. We analyzed some simple mathematical models and generalized the study to understand the growth of tumor cells. The main proposed model is a system of ordinary differential equations which combines interactions among natural killer cells, dendritic cells and cytotoxic CD8+T cells. The model is solved numerically to explain how the tumor cells spread and become more dangerous as well as the treatment process of cancer. It is also studied that how the cell behaves in the presence of different therapy and drugs. The optimal control of chemotherapy has been discussed. It has also been explained how much the model is effective in reducing tumor cells over time. Finally, a couple of spatially distributed models are discussed for tumor cell growth.

Keywords: Mathematical models; tumor growth; chemotherapy; di usion; optimal control

© International Journal of Ground Sediment & Water, ©Sun Jichao.

The website is

Files (3.0 MB)
Name Size
3.0 MB Download
All versions This version
Views 152152
Downloads 103103
Data volume 310.3 MB310.3 MB
Unique views 122122
Unique downloads 9595


Cite as