MIVEGEC, IRD, CNRS, Univ. Montpellier, Montpellier, France.
J Math Biol. 2021 Feb 5;82(3):16. doi: 10.1007/s00285-021-01571-9.
The evolution and emergence of antibiotic resistance is a major public health concern. The understanding of the within-host microbial dynamics combining mutational processes, horizontal gene transfer and resource consumption, is one of the keys to solving this problem. We analyze a generic model to rigorously describe interactions dynamics of four bacterial strains: one fully sensitive to the drug, one with mutational resistance only, one with plasmidic resistance only, and one with both resistances. By defining thresholds numbers (i.e. each strain's effective reproduction and each strain's transition threshold numbers), we first express conditions for the existence of non-trivial stationary states. We find that these thresholds mainly depend on bacteria quantitative traits such as nutrient consumption ability, growth conversion factor, death rate, mutation (forward or reverse), and segregational loss of plasmid probabilities (for plasmid-bearing strains). Next, concerning the order in the set of strain's effective reproduction thresholds numbers, we show that the qualitative dynamics of the model range from the extinction of all strains, coexistence of sensitive and mutational resistance strains, to the coexistence of all strains at equilibrium. Finally, we go through some applications of our general analysis depending on whether bacteria strains interact without or with drug action (either cytostatic or cytotoxic).
抗生素耐药性的进化和出现是一个主要的公共卫生关注点。理解宿主内微生物动态，包括突变过程、水平基因转移和资源消耗，是解决这一问题的关键之一。我们分析了一个通用模型，以严格描述四种细菌菌株的相互作用动态：一种对药物完全敏感，一种只有突变耐药性，一种只有质粒耐药性，一种同时具有两种耐药性。通过定义阈值数量（即每种菌株的有效繁殖和每种菌株的转变阈值数量），我们首先表达了存在非平凡静态状态的条件。我们发现这些阈值主要取决于细菌的定量特征，如营养物质消耗能力、生长转化率、死亡率、突变（正向或反向）和质粒分离丢失的概率（对于携带质粒的菌株）。接下来，关于菌株有效繁殖阈值数量的顺序，我们表明模型的定性动力学范围从所有菌株的灭绝、敏感和突变耐药菌株的共存，到所有菌株在平衡时的共存。最后，我们根据细菌菌株是否在没有或有药物作用（细胞抑制或细胞毒性）的情况下相互作用，对我们的一般分析进行了一些应用。
