Population Dynamics Model and Analysis for Bacteria Transformation and Conjugation

TL;DR

This paper develops a mathematical model for bacteria population dynamics incorporating transformation and conjugation, revealing their individual and combined effects on bacterial coexistence and oscillations, with ecological implications.

Contribution

It introduces a novel two-species population model that explicitly includes transformation and conjugation mechanisms, analyzing their separate and combined impacts.

Findings

Transformation leads to extinction or stable coexistence.

Conjugation causes oscillatory population dynamics.

Combined effects determine regimes of stable coexistence.

Abstract

We present a two-species population model in a well-mixed environment where the dynamics involves, in addition to birth and death, changes due to environmental factors and inter-species interactions. The novel dynamical components are motivated by two common mechanisms for developing antibiotic resistance in bacteria: plasmid {\it transformation}, where external genetic material in the form of a plasmid is transferred inside a host cell; and {\it conjugation} by which one cell transfers genetic material to another by direct cell-to-cell contact. Through analytical and numerical methods, we identify the effects of transformation and conjugation individually. With transformation only, the two-species system will evolve towards one species' extinction, or a stable co-existence in the long-time limit. With conjugation only, we discover interesting oscillations for the system. Further, we quantify the combined effects of transformation and conjugation, and chart the regimes of stable co-existence, a result with ecological implications.