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

Ardak Kashkynbayev, Yerlan Amanbek, Bibinur Shupeyeva, Yang Kuang

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish (US)
Pages (from-to)7234-7247
Number of pages14
JournalMathematical Biosciences and Engineering
Volume17
Issue number6
DOIs
StatePublished - Oct 23 2020

Keywords

  • Glioblastoma
  • Reaction-diffusion equation
  • Stability
  • Traveling wave solution
  • Tumor growth

ASJC Scopus subject areas

  • Modeling and Simulation
  • Agricultural and Biological Sciences(all)
  • Computational Mathematics
  • Applied Mathematics

Fingerprint

Dive into the research topics of 'Existence of traveling wave solutions to data-driven glioblastoma multiforme growth models with density-dependent diffusion'. Together they form a unique fingerprint.

Cite this