A Model of Band-Pass Phenotypic Resistance in a Modified Beverton-Holt Framework
Antibiotic resistance, Beverton-Holt, Band-Pass
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.
Nemzer, L. R. (2014). A Model of Band-Pass Phenotypic Resistance in a Modified Beverton-Holt Framework. Mathematical Biosciences, 252, 7 - 13. https://doi.org/10.1016/j.mbs.2014.03.003. Retrieved from https://nsuworks.nova.edu/cnso_chemphys_facarticles/89