Institute for Evolution and Biodiversity, University of Münster, Münster, Germany.
Institute of Ecology and Environmental Sciences of Paris, Sorbonne Université, UPEC, CNRS, IRD, INRA, Paris, France.
PLoS Comput Biol. 2023 Aug 14;19(8):e1011364. doi: 10.1371/journal.pcbi.1011364. eCollection 2023 Aug.
The use of an antibiotic may lead to the emergence and spread of bacterial strains resistant to this antibiotic. Experimental and theoretical studies have investigated the drug dose that minimizes the risk of resistance evolution over the course of treatment of an individual, showing that the optimal dose will either be the highest or the lowest drug concentration possible to administer; however, no analytical results exist that help decide between these two extremes. To address this gap, we develop a stochastic mathematical model of bacterial dynamics under antibiotic treatment. We explore various scenarios of density regulation (bacterial density affects cell birth or death rates), and antibiotic modes of action (biostatic or biocidal). We derive analytical results for the survival probability of the resistant subpopulation until the end of treatment, the size of the resistant subpopulation at the end of treatment, the carriage time of the resistant subpopulation until it is replaced by a sensitive one after treatment, and we verify these results with stochastic simulations. We find that the scenario of density regulation and the drug mode of action are important determinants of the survival of a resistant subpopulation. Resistant cells survive best when bacterial competition reduces cell birth and under biocidal antibiotics. Compared to an analogous deterministic model, the population size reached by the resistant type is larger and carriage time is slightly reduced by stochastic loss of resistant cells. Moreover, we obtain an analytical prediction of the antibiotic concentration that maximizes the survival of resistant cells, which may help to decide which drug dosage (not) to administer. Our results are amenable to experimental tests and help link the within and between host scales in epidemiological models.
抗生素的使用可能导致对抗生素具有耐药性的细菌菌株的出现和传播。实验和理论研究已经研究了在个体治疗过程中使耐药性进化风险最小化的药物剂量，表明最佳剂量将是最高或最低的可能施药药物浓度；但是，不存在有助于在这两个极端之间做出选择的分析结果。为了解决这一差距，我们开发了一种抗生素治疗下细菌动力学的随机数学模型。我们探讨了密度调节（细菌密度影响细胞出生率或死亡率）和抗生素作用模式（抑菌或杀菌）的各种情况。我们得出了耐药亚群在治疗结束时的生存概率、治疗结束时耐药亚群的大小、耐药亚群在治疗后被敏感亚群取代之前的携带时间的分析结果，并通过随机模拟验证了这些结果。我们发现，密度调节的情况和药物作用模式是耐药亚群生存的重要决定因素。当细菌竞争降低细胞出生率并且使用杀菌抗生素时，耐药细胞的存活最佳。与类似的确定性模型相比，到达的耐药型种群规模更大，并且由于耐药细胞的随机丢失，携带时间略有减少。此外，我们获得了最大程度地提高耐药细胞生存能力的抗生素浓度的分析预测，这可能有助于决定（不）给予哪种药物剂量。我们的结果适合进行实验测试，并有助于将流行模型中的宿主内和宿主间尺度联系起来。
