A hyperbolic model of chemotaxis on a network: a numerical study

TL;DR

This paper develops a numerical scheme for a hyperbolic chemotaxis model on networks, ensuring mass conservation and accurate source term approximation, with applications in tissue engineering and wound healing.

Contribution

It introduces a novel numerical scheme for hyperbolic chemotaxis models on networks that guarantees mass conservation and accurately captures source effects at equilibrium.

Findings

The scheme conserves total mass globally.

Numerical tests demonstrate stability and accuracy.

The model effectively simulates chemotactic behavior on networks.

Abstract

In this paper we deal with a semilinear hyperbolic chemotaxis model in one space dimension evolving on a network, with suitable transmission conditions at nodes. This framework is motivated by tissue-engineering scaffolds used for improving wound healing. We introduce a numerical scheme, which guarantees global mass densities conservation. Moreover our scheme is able to yield a correct approximation of the effects of the source term at equilibrium. Several numerical tests are presented to show the behavior of solutions and to discuss the stability and the accuracy of our approximation.