A tumor growth model with chemotherapy and diffusion effect

Volume 21, Issue 1, pp 57--68 http://dx.doi.org/10.22436/jmcs.021.01.06

Publication Date: March 22, 2020 Submission Date: November 24, 2019 Revision Date: February 06, 2020 Accteptance Date: February 12, 2020

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Authors

I. J. T. R. Tamsih - Department of Mathematics, Faculty of Natural Science, University of Brawijaya, Indonesia. T. Trisilowati - Department of Mathematics, Faculty of Natural Science, University of Brawijaya, Indonesia. U. Habibah - Department of Mathematics, Faculty of Natural Science, University of Brawijaya, Indonesia.

Abstract

Chemotherapy is the most common treatment for cancer by using certain drugs or hormones. One of the mechanisms to transport the drugs within the human body is called diffusion-passive transport where the substances move from an area of high concentration to an area of low concentration. By adding chemotherapy and the diffusion effect, a model of tumor growth and its interaction with some types of immune cell such as macrophages, CD8+T and IFN-\(\gamma\) is studied. Regarding to the analysis result, the existence of tumor equilibrium point is determined by Cardan's condition. It is locally asymptotically stable if it satisfies the Routh-Hurwitz criterion. Furthermore, the simulation shows that we can eliminate more tumor cell by extending the duration of chemotherapy injection and shortening the interval of chemotherapy. However, these methods are not effective in the long term. It is also observed that the value of the diffusion coefficient affects the growth of the tumor and other cells.

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Keywords

• Tumor
• immune cell
• diffusion
• chemotherapy
• dynamical analysis

MSC

•  92B05
•  49K15
•  49K20

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