Abstract
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.
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P. De Leenheer was supported in part by NSF grant DMS-0614651. T. Gedeon was supported in part by NSF grant DMS-0818785. S. S. Pilyugin was supported in part by NSF grant DMS-0818050.
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De Leenheer, P., Dockery, J., Gedeon, T. et al. Senescence and antibiotic resistance in an age-structured population model. J. Math. Biol. 61, 475–499 (2010). https://doi.org/10.1007/s00285-009-0302-7
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DOI: https://doi.org/10.1007/s00285-009-0302-7