De Leenheer Patrick, Dockery Jack, Gedeon Tomás, Pilyugin Sergei S
Department of Mathematics, University of Florida, Gainesville, FL, 32611-8105, USA.
J Math Biol. 2010 Oct;61(4):475-99. doi: 10.1007/s00285-009-0302-7. Epub 2009 Nov 12.
Different theories have been proposed to understand the growing problem of antibiotic resistance of microbial populations. Here we investigate a model that is based on the hypothesis that senescence is a possible explanation for the existence of so-called persister cells which are resistant to antibiotic treatment. We study a chemostat model with a microbial population which is age-structured and show that if the growth rates of cells in different age classes are sufficiently close to a scalar multiple of a common growth rate, then the population will globally stabilize at a coexistence steady state. This steady state persists under an antibiotic treatment if the level of antibiotics is below a certain threshold; if the level exceeds this threshold, the washout state becomes a globally attracting equilibrium.
为理解微生物群体抗生素耐药性这一日益严重的问题，人们提出了不同的理论。在此，我们研究一个基于如下假设的模型：衰老可能是所谓的持久性细胞存在的一种解释，这些持久性细胞对抗生素治疗具有抗性。我们研究一个具有年龄结构的微生物群体的恒化器模型，并表明如果不同年龄组细胞的生长速率足够接近一个共同生长速率的标量倍数，那么该群体将在共存稳态下全局稳定。如果抗生素水平低于某个阈值，这种稳态在抗生素治疗下会持续存在；如果水平超过该阈值，洗出状态将成为全局吸引的平衡点。
