Mathematical analysis and numerical simulation of a tumor-host model with chemotherapy application
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Date
2018
Journal Title
Journal ISSN
Volume Title
Publisher
Tianjin Polytechnic University
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.
Description
Keywords
Anti-angiogenic therapy, Cytotoxic therapy, Stability analysis, Mathematical modelling
Citation
Kolade, M. et al. 2018. Mathematical analysis and numerical simulation of a tumor-host model with chemotherapy application. Commun. Math. Biol. Neurosci. 2018:21. doi: https://doi.org/10.28919/cmbn/3865