Probability of Antibiotic Resistance During Treatment in Stochastic PK/PD-Based Bacterial Model with Distinct Drug and Mutation Modes

Technical Summary

Problem Statement
The evolution of antibiotic resistance is a critical challenge in infectious disease management. While mathematical models, particularly those utilizing differential equations and stochastic processes, have been widely employed to study this phenomenon, existing frameworks often rely on the assumption of "standing genetic variation." This approach presumes that resistant strains are already present within the bacterial population at the onset of treatment. Consequently, these models frequently overlook the stochastic nature of de novo resistance emergence, specifically the random or drug-induced mutation of reference (sensitive) bacterial strains during the course of therapy. This gap limits the ability to accurately predict resistance probabilities under dynamic treatment conditions where new mutations arise.

Methodology
To address these limitations, the authors propose a novel pharmacokinetics/pharmacodynamics (PK/PD)-based continuous-time Markov chain model. This framework explicitly simulates the competition and mutation dynamics between sensitive and resistant bacterial subpopulations within an infected host during antibiotic treatment. The model incorporates distinct modes of drug action and mutation mechanisms.

Mathematically, the proposed Markov chain is approximated as a generalized birth–death process with immigration. This approximation is crucial as it facilitates the explicit derivation of the probability that a resistant bacterial population will successfully establish itself during the treatment window. The model is designed to capture the inherent stochasticity of de novo emergence while simultaneously accounting for several biological and pharmacological variables:

• Different antibiotic modes of action (biostatic vs. biocidal).
• Horizontal gene transfer.
• Nutrient availability.
• Drug pharmacokinetics.

Key Contributions and Results
The primary contribution of this work is the derivation of an explicit probability for the establishment of resistance, moving beyond models that assume pre-existing resistance. By integrating de novo mutation into the stochastic framework, the authors explore how various factors influence resistance outcomes.

The analysis yields several specific findings:

1. Drug Mode of Action: The study finds that replication-targeting drugs (biostatic) are more effective at suppressing resistance compared to death-targeting drugs (biocidal).
2. Drug Concentration Dynamics: Consistent with prior literature, the model identifies that resistance is maximized at intermediate drug concentrations.
3. Impact of De Novo Mutation: A critical distinction in this work is the observation that when de novo mutation is considered, the superiority of higher drug doses in preventing resistance emergence is magnified. This suggests that the risk of new mutations arising during treatment significantly alters the optimal dosing strategy compared to models relying solely on standing variation.

Significance
The paper positions its significance in refining the understanding of antibiotic resistance evolution by shifting the focus from static pre-existing populations to dynamic, stochastic emergence. By explicitly modeling the probability of de novo resistance establishment within a PK/PD context, the work provides a more comprehensive tool for evaluating treatment strategies. It highlights that the consideration of mutation modes and drug pharmacokinetics is essential for accurately predicting resistance risks, particularly regarding the comparative efficacy of different drug classes and dosing regimens.