10.5281/zenodo.4275629
https://zenodo.org/records/4275629
oai:zenodo.org:4275629
Jannatun Irana Ira
Jannatun Irana Ira
Department of Mathematics, University of Dhaka, Bangladesh
Md. Shahidul Islam
Md. Shahidul Islam
Department of Mathematics, University of Dhaka, Bangladesh
J C Misra
J C Misra
Centre for Healthcare Science and Technology, Indian Institute of Engineering Science and Technology, India
Md. Kamrujjaman
Md. Kamrujjaman
Department of Mathematics, University of Dhaka, Bangladesh & Department of Mathematics and Statistics, University of Calgary, Canada
Mathematical Modelling of the Dynamics of Tumor Growth and its Optimal Control
Zenodo
2020
Mathematical models
tumor growth
chemotherapy
diffusion
optimal control
2020-11-16
eng
10.5281/zenodo.4275628
Creative Commons Attribution 4.0 International
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
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