Existence of traveling wave solutions to data-driven glioblastoma multiforme growth models with density-dependent diffusion

Ardak Kashkynbayev; Yerlan Amanbek; Bibinur Shupeyeva; Yang Kuang; Ardak Kashkynbayev; Yerlan Amanbek; Bibinur Shupeyeva; Yang Kuang

doi:10.3934/mbe.2020371

Mathematical Biosciences and Engineering

2020, Volume 17, Issue 6: 7234-7247. doi: 10.3934/mbe.2020371

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Research article

Existence of traveling wave solutions to data-driven glioblastoma multiforme growth models with density-dependent diffusion

1.
Department of Mathematics, Nazarbayev University, 010000 Nur-Sultan, Kazakhstan
2.
School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ 85287, USA
† Contributed equally as the first author

Received: 21 September 2020 Accepted: 15 October 2020 Published: 23 October 2020

Mathematical modeling for cancerous disease has attracted increasing attention from the researchers around the world. Being an effective tool, it helps to describe the processes that happen to the tumour as the diverse treatment scenarios. In this paper, a density-dependent reaction-diffusion equation is applied to the most aggressive type of brain cancer, Glioblastoma multiforme. The model contains the terms responsible for the growth, migration and proliferation of the malignant tumour. The traveling wave solution used is justified by stability analysis. Numerical simulation of the model is provided and the results are compared with the experimental data obtained from the reference papers.
- reaction-diffusion equation,
- traveling wave solution,
- glioblastoma,
- tumor growth,
- stability
Citation: Ardak Kashkynbayev, Yerlan Amanbek, Bibinur Shupeyeva, Yang Kuang. Existence of traveling wave solutions to data-driven glioblastoma multiforme growth models with density-dependent diffusion[J]. Mathematical Biosciences and Engineering, 2020, 17(6): 7234-7247. doi: 10.3934/mbe.2020371

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Abstract

Mathematical modeling for cancerous disease has attracted increasing attention from the researchers around the world. Being an effective tool, it helps to describe the processes that happen to the tumour as the diverse treatment scenarios. In this paper, a density-dependent reaction-diffusion equation is applied to the most aggressive type of brain cancer, Glioblastoma multiforme. The model contains the terms responsible for the growth, migration and proliferation of the malignant tumour. The traveling wave solution used is justified by stability analysis. Numerical simulation of the model is provided and the results are compared with the experimental data obtained from the reference papers.

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