Department of Mathematics, Lahore University of Management Sciences, Lahore, Pakistan.
Department of Mathematics and Sciences, Ajman University, Ajman, UAE.
PLoS One. 2022 Oct 10;17(10):e0275762. doi: 10.1371/journal.pone.0275762. eCollection 2022.
Mathematical models can be very useful in determining efficient and successful antibiotic dosing regimens. In this study, we consider the problem of determining optimal antibiotic dosing when bacteria resistant to antibiotics are present in addition to susceptible bacteria. We consider two different models of resistance acquisition, both involve the horizontal transfer (HGT) of resistant genes from a resistant to a susceptible strain. Modeling studies on HGT and study of optimal antibiotic dosing protocols in the literature, have been mostly focused on transfer of resistant genes via conjugation, with few studies on HGT via transformation. We propose a deterministic ODE based model of resistance acquisition via transformation, followed by a model that takes into account resistance acquisition through conjugation. Using a numerical optimization algorithm to determine the 'best' antibiotic dosing strategy. To illustrate our optimization method, we first consider optimal dosing when all the bacteria are susceptible to the antibiotic. We then consider the case where resistant strains are present. We note that constant periodic dosing may not always succeed in eradicating the bacteria while an optimal dosing protocol is successful. We determine the optimal dosing strategy in two different scenarios: one where the total bacterial population is to be minimized, and the next where we want to minimize the bacterial population at the end of the dosing period. We observe that the optimal strategy in the first case involves high initial dosing with dose tapering as time goes on, while in the second case, the optimal dosing strategy is to increase the dosing at the beginning of the dose cycles followed by a possible dose tapering. As a follow up study we intend to look at models where 'persistent' bacteria may be present in additional to resistant and susceptible strain and determine the optimal dosing protocols in this case.
数学模型在确定有效和成功的抗生素剂量方案方面非常有用。在这项研究中，我们考虑了在除了敏感细菌之外还存在对抗生素具有抗性的细菌时确定最佳抗生素剂量的问题。我们考虑了两种不同的耐药性获得模型，这两种模型都涉及到耐药基因从耐药菌向敏感菌的水平转移（HGT）。HGT 建模研究和文献中关于最佳抗生素剂量方案的研究主要集中在通过接合转移耐药基因，而通过转化转移耐药基因的研究较少。我们提出了一种基于确定性 ODE 的通过转化获得耐药性的模型，然后提出了一种考虑通过接合获得耐药性的模型。使用数值优化算法来确定“最佳”抗生素剂量策略。为了说明我们的优化方法，我们首先考虑当所有细菌都对抗生素敏感时的最佳剂量。然后我们考虑存在耐药菌株的情况。我们注意到，恒定期量给药可能并不总是能成功消灭细菌，而最佳给药方案则是成功的。我们在两种不同情况下确定最佳给药策略：一种是使总细菌种群最小化，另一种是在给药期结束时使细菌种群最小化。我们观察到，第一种情况下的最佳策略涉及初始高剂量给药，随着时间的推移逐渐减少剂量，而在第二种情况下，最佳给药策略是在剂量周期开始时增加给药，然后可能减少剂量。作为后续研究，我们打算研究除了耐药菌和敏感菌之外还存在“持续”细菌的模型，并在这种情况下确定最佳给药方案。
