A fitted operator method for tumor cells dynamics in their micro-environment
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Date
2019
Journal Title
Journal ISSN
Volume Title
Publisher
Tianjin Polytechnic University
Abstract
In this paper, we consider a quasi non-linear reaction-diffusion model designed to mimic tumor cells’
proliferation and migration under the influence of their micro-environment in vitro. Since the model can be used
to generate hypotheses regarding the development of drugs which confine tumor growth, then considering the
composition of the model, we modify the model by incorporating realistic effects which we believe can shed more
light into the original model. We do this by extending the quasi non-linear reaction-diffusion model to a system
of discrete delay quasi non-linear reaction-diffusion model. Thus, we determine the steady states, provide the
conditions for global stability of the steady states by using the method of upper and lower solutions and analyze
the extended model for the existence of Hopf bifurcation and present the conditions for Hopf bifurcation to occur.
Since it is not possible to solve the models analytically, we derive, analyze, implement a fitted operator method
and present our results for the extended model. Our numerical method is analyzed for convergence and we find
that is of second order accuracy. We present our numerical results for both of the models for comparison purposes.
Description
Keywords
Tumor cells, Micro-environment, Hopf bifurcation, Stability analysis, Numerical methods, Mathematical modelling
Citation
Kolade, M. 2019. A fitted operator method for tumor cells dynamics in their micro-environment. Commun. Math. Biol. Neurosci. 2019:18. doi: https://doi.org/10.28919/cmbn/3885