Bacterial plasmids play a fundamental role in antibiotic resistance. However, a lack of knowledge about their biology is an obstacle in fully understanding the mechanisms and properties of plasmid-mediated resistance. This has motivated investigations of real systems in vitro to analyze the transfer and replication of plasmids. In this work, we address this issue with mathematical modeling. We formulate and perform a qualitative analysis of a nonlinear system of ordinary differential equations describing the competition dynamics between plasmids and sensitive and resistant bacteria. In addition, we estimated parameter values from empirical data. Our model predicts scenarios consistent with biological phenomena. The elimination or spread of infection depends on factors associated with bacterial reproduction and the transfer and replication of plasmids. From the estimated parameters, three bacterial growth experiments were analyzed in vitro. We determined the experiment with the highest bacterial growth rate and the highest rate of plasmid transfer. Moreover, numerical simulations were performed to predict bacterial growth.

中文翻译：

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考虑质粒复制的一般性大规模作用定律的细菌抗性模型

细菌质粒在抗生素耐药性中发挥着重要作用。然而，缺乏对其生物学的了解是充分理解质粒介导的抗性机制和特性的障碍。这激发了对真实系统的研究体外分析质粒的转移和复制。在这项工作中，我们通过数学建模来解决这个问题。我们制定并执行描述质粒与敏感和耐药细菌之间的竞争动态的常微分方程非线性系统的定性分析。此外，我们根据经验数据估计参数值。我们的模型预测与生物现象一致的情景。感染的消除或传播取决于与细菌繁殖以及质粒的转移和复制相关的因素。从估计的参数，分析了三个细菌生长实验体外. 我们确定了具有最高细菌生长率和最高质粒转移率的实验。此外，进行数值模拟以预测细菌生长。