Version 1
: Received: 21 April 2020 / Approved: 22 April 2020 / Online: 22 April 2020 (06:04:35 CEST)
Version 2
: Received: 3 July 2020 / Approved: 5 July 2020 / Online: 5 July 2020 (16:39:32 CEST)
How to cite:
Irana Ira, J.; Islam, M.S.; Misra, J.C.; Kamrujjaman, M. Mathematical Modelling of the Dynamics of Tumor Growth and its Optimal Control. Preprints2020, 2020040391
Irana Ira, J.; Islam, M.S.; Misra, J.C.; Kamrujjaman, M. Mathematical Modelling of the Dynamics of Tumor Growth and its Optimal Control. Preprints 2020, 2020040391
Irana Ira, J.; Islam, M.S.; Misra, J.C.; Kamrujjaman, M. Mathematical Modelling of the Dynamics of Tumor Growth and its Optimal Control. Preprints2020, 2020040391
APA Style
Irana Ira, J., Islam, M.S., Misra, J.C., & Kamrujjaman, M. (2020). Mathematical Modelling of the Dynamics of Tumor Growth and its Optimal Control. Preprints. https://doi.org/
Chicago/Turabian Style
Irana Ira, J., Jagadis Chandra Misra and Md. Kamrujjaman. 2020 "Mathematical Modelling of the Dynamics of Tumor Growth and its Optimal Control" Preprints. https://doi.org/
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 cytotoxicCD8+ 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; diffusion; optimal control
Subject
Medicine and Pharmacology, Oncology and Oncogenics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Commenter: Jannatun Irana Ira
Commenter's Conflict of Interests: Author