Global stability in a negative chemotaxis system with chemically induced lethality

TL;DR

This paper analyzes a chemotaxis model with negative chemotaxis, logistic growth, and cell death, showing conditions for population extinction or stabilization to a steady state.

Contribution

It provides a rigorous analysis of the long-term behavior of a chemotaxis system with lethal chemorepellent, highlighting the impact of chemorepellent levels.

Findings

Solutions tend to extinction or steady state depending on chemorepellent magnitude.

The model captures the effects of self-produced and externally supplied lethal chemorepellent.

Long-time dynamics are characterized in terms of population stability.

Abstract

In this paper, we investigate the long-time dynamics of a repulsive Keller-Segel chemotaxis system. The model features negative chemotaxis, logistic growth and a cell death term, accounting for a lethal chemorepellent that is self-produced by the cells and externally supplied. We prove that, for constant chemorepellent supplies, depending on their magnitude with respect to the logistic growth rate, solutions converge in $L^\infty$ norm toward extinction of the population, or equilibrate toward a nontrivial spatially homogeneous steady state.