Mathematical analysis and numerical simulation of a tumor-host model with chemotherapy application

Kolade M. Owolabi, Kailash C. Patidar, Albert Shikongo

Abstract


In this paper, a system of non-linear quasi-parabolic partial differential system, modeling the chemotherapy application of spatial tumor-host interaction is considered. At some certain parameters, we derive the steady state of the anti-angiogenic therapy, baseline therapy and anti-cytotoxic therapy models as well as their local stability condition. We use the method of upper and lower solutions to show that the steady states are globally stable. Since the system of non-linear quasi-parabolic partial differential cannot be solved analytically, we formulate a robust numerical scheme based on the semi-fitted finite difference operator. Analysis of the basic properties of the method shows that it is consistent, stable and convergent. Our numerical results are in agreement with our theoretical findings.

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Published: 2018-11-16

How to Cite this Article:

Kolade M. Owolabi, Kailash C. Patidar, Albert Shikongo, Mathematical analysis and numerical simulation of a tumor-host model with chemotherapy application, Communications in Mathematical Biology and Neuroscience, Vol 2018 (2018), Article ID 21

Copyright © 2018 Kolade M. Owolabi, Kailash C. Patidar, Albert Shikongo. 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.

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