Growth of a population of bacteria in a dynamical hostile environment

TL;DR

This paper models bacterial growth within a dynamically hostile environment, using percolation theory to demonstrate conditions under which bacteria can grow linearly despite immune system defenses.

Contribution

It introduces new tools for analyzing dependent percolation models derived from renormalization, specifically applied to bacterial growth in immune environments.

Findings

Bacterial population grows linearly under certain parameters.

Immune response modeled as subcritical percolation clusters.

Development of general tools for dependent percolation analysis.

Abstract

We study the growth of a population of bacteria in a dynamical hostile environment corresponding to the immune system of the colonised organism. The immune cells evolve as subcritical open clusters of oriented percolation and are perpetually reinforced by an immigration process, while the bacteria try to grow as a supercritical oriented percolation in the remaining empty space. For appropriate values of the parameters, we prove that the population of bacteria grows linearly. In this perspective, we build general tools to study dependent percolation models issued from renormalization processes.