Stochastic modeling of in vitro bactericidal potency

TL;DR

This paper introduces a stochastic Galton--Watson model to analyze bacterial growth under antibiotics, providing estimators for key pharmacological parameters and demonstrating excellent fit to experimental data.

Contribution

The paper develops a new probabilistic model for bacterial growth under antibiotics and offers estimators for MIC and model parameters, validated with real biological data.

Findings

Model fits well to experimental data

Provided estimators are asymptotically normal

Effective for analyzing antibiotic efficacy

Abstract

We provide a Galton--Watson model for the growth of a bacterial population in the presence of antibiotics. We assume that bacterial cells either die or duplicate, and the corresponding probabilities depend on the concentration of the antibiotic. Assuming that the mean offspring number is given by $m(c) = 2 / (1 + \alpha c^\beta)$ for some $\alpha, \beta$, where $c$ stands for the antibiotic concentration we obtain weakly consistent, asymptotically normal estimator both for $(\alpha, \beta)$ and for the minimal inhibitory concentration (MIC), a relevant parameter in pharmacology. We apply our method to real data, where \emph{Chlamydia trachomatis} bacteria was treated by azithromycin and ciprofloxacin. For the measurements of \emph{Chlamydia} growth quantitative PCR technique was used. The 2-parameter model fits remarkably well to the biological data.