On an age and spatially structured population model for Proteus Mirabilis swarm-colony development

TL;DR

This paper investigates a mathematical model combining differential equations to explain the regular spatial-temporal patterns formed by Proteus mirabilis bacteria during swarm-colony development.

Contribution

It introduces a coupled ODE-PDE model with aging and nonlinear diffusion, proving the existence of global weak solutions for the first time.

Findings

Model reproduces observed bacterial patterns.

Proves existence of global weak solutions.

Provides a mathematical framework for bacterial pattern formation.

Abstract

Proteus mirabilis are bacteria that make strikingly regular spatial-temporal patterns on agar surfaces. In this paper we investigate a mathematical model that has been shown to display these structures when solved numerically. The model consists of an ordinary differential equation coupled with a partial differential equation involving a first-order hyperbolic aging term together with nonlinear degenerate diffusion. The system is shown to admit global weak solutions.