Mathematical modeling and analysis of a tumor invasion problem with angiogenesis and taxis cascade

Christina Surulescu; Michael Winkler

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arXiv · 2412.04038

Mathematical modeling and analysis of a tumor invasion problem with angiogenesis and taxis cascade

Christina Surulescu·Michael Winkler

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Abstract

We propose a mathematical model for tumor invasion supported by angiogenesis and interactions with the surrounding tissue. For the model deduction we employ a multiscale approach starting from lower scales and obtaining by an informal parabolic upscaling a system of reaction-diffusion-taxis equations with a so-called 'taxis cascade', where one species is performing taxis towards a signal whose production/decay is controled by the other, for which it also serves as a tactic cue. We prove global existence and uniqueness of solutions to the obtained PDE-ODE system and perform numerical simulations to illustrate the behavior of solutions.

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Christina Surulescu, Michael Winkler. 2024-12-05. Mathematical modeling and analysis of a tumor invasion problem with angiogenesis and taxis cascade. https://arxiv.org/abs/2412.04038

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