A model of band-pass phenotypic resistance in a modified Beverton–Holt framework

• A mathematical model of a periodically applied antibiotic is introduced.
• Band-pass behavior is possible, in which survival is at intermediate periods only.
• If the antibiotic concentration is too low, the colony survives even long periods.

A new mathematical model of phenotypic bacterial resistance to a periodically applied antibiotic is presented. Using a modified Beverton–Holt framework, and without appealing to any explicit internal timescale or heritable mutations, we map the parameter-space regions corresponding to bacterial colony survival or extinction. It is demonstrated that band-pass behavior, in which colony survival occurs at intermediate – but not short or long – antibiotic application periods, is a possible regime for some initial population values if the bactericidal activity is sufficient. However, below this threshold value of antibiotic efficacy, a “fixed-point catastrophe” occurs, and colony extinction does not occur when the bacteria are challenged with long application periods. These results suggest that the dosing schedule of antibiotics within a clinical setting merits additional scrutiny, since even seemingly unimportant modifications to the frequency of administration may lead to widely diverging patient outcomes.

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