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Number 4 - December 2023
Volume 33 - 2023
Travelling waves for low-grade glioma growth and response to a chemotherapy model
Agnieszka Bartłomiejczyk, Marek Bodnar, Magdalena U. Bogdańska, Monika J. Piotrowska
Abstract
Low-grade gliomas (LGGs) are primary brain tumours which evolve very slowly in time, but inevitably cause patient
death. In this paper, we consider a PDE version of the previously proposed ODE model that describes the changes in the
densities of functionally alive LGGs cells and cells that are irreversibly damaged by chemotherapy treatment. Besides the
basic mathematical properties of the model, we study the possibility of the existence of travelling wave solutions in the
framework of Fenichel’s invariant manifold theory. The estimates of the minimum speeds of the travelling wave solutions
are provided. The obtained analytical results are illustrated by numerical simulations.
Keywords
glioma, tumour, generalized model, treatment, partial differential equations, wave solutions, chemotherapy