Modeling Heterogeneous Bacterial Populations Exposed to Antibiotics: The Logistic-Dynamics Case

In typical in vitro tests for clinical use or development of antibiotics, samples from a bacterial population are exposed to an antibiotic at various concentrations. The resulting data can then be used to build a mathematical model suitable for dosing regimen design or for further development. For bacterial populations that include resistant subpopulations-an issue that has reached alarming proportions-building such a model is challenging. In prior work, we developed a related modeling framework for such heterogeneous bacterial populations following linear dynamics when exposed to an antibiotic. We extend this framework to the case of logistic dynamics, common among strongly resistant bacterial strains. Explicit formulas are developed that can be easily used in parameter estimation and subsequent dosing regimen design under realistic pharmacokinetic conditions. A case study using experimental data from the effect of an antibiotic on a gram-negative bacterial population exemplifies the usefulness of the proposed approach.