Working Paper Article Version 2 This version is not peer-reviewed

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

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. 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. Preprints 2020, 2020040391

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.

Subject Areas

Mathematical models; tumor growth; chemotherapy; diffusion; optimal control

Comments (1)

Comment 1
Received: 5 July 2020
Commenter: Jannatun Irana Ira
Commenter's Conflict of Interests: Author
Comment: The abstract and format have been updated and one co-author has been added.
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