Senescence and antibiotic resistance in an age-structured population model
De Leenheer, Patrick
Dockery, Jack D.
Pilyugin, Sergei S.
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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.
P. De Leenheer, J. Dockery, T. Gedeon and S. Pilyugin, “Senescence and antibiotic resistance in an age-structured population model”, J. Math. Biol., 61(4), pp. 475-499, (October 2010).