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 transformation , where external genetic material in the form of a plasmid is transferred inside a host cell; and 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 stab...

中文翻译：

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细菌转化与结合的种群动力学模型与分析

我们提出了一个在充分混合的环境中的两种种群模型，其中除了出生和死亡外，动力学还涉及由于环境因素和种间相互作用而引起的变化。新颖的动力学成分是由两种在细菌中产生抗生素抗性的常见机制所激发：质粒转化，其中质粒形式的外部遗传物质在宿主细胞内转移；和结合，一种细胞通过直接的细胞间接触将遗传物质转移到另一种细胞上。通过分析和数值方法，我们分别确定了变换和共轭的影响。仅通过转化，两个物种的系统便会朝着一个物种的灭绝或长期稳定的共存进化。仅使用共轭，我们发现了系统的有趣振荡。此外，我们量化了变换和共轭的组合效应，并绘制了稳定状态的图表。