We formulate a system of ordinary differential equations to model the contribution of antibiotic treatment and immune system to combat bacterial infections. We obtained threshold conditions that determine when the bacteria can be eliminated, which are consistent with biological phenomena. In order to minimize the bacterial population, we formulated an optimal control problem considering the action of both antibiotic and immune system. The optimal control is obtained applying the Pontryagin’s Principle. The results show the relevance of the synergism between the antibiotic treatment and the immune system response.

中文翻译：

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应用于质粒介导的抗生素抗性的最优控制问题

我们制定了一个常微分方程系统来模拟抗生素治疗和免疫系统对抗细菌感染的贡献。我们获得了确定何时可以消除细菌的阈值条件，这与生物学现象是一致的。为了最大限度地减少细菌数量，我们制定了一个考虑抗生素和免疫系统作用的最佳控制问题。最佳控制是应用庞特里亚金原理获得的。结果显示了抗生素治疗与免疫系统反应之间协同作用的相关性。