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

Optimizing Antimicrobial Treatment Schedules: Some Fundamental Analytical Results

This work studies fundamental questions regarding the optimal design of antimicrobial treatment protocols, using pharmacodynamic and pharmacokinetic mathematical models. We consider the problem of designing an antimicrobial treatment schedule to achieve eradication of a microbial infection, while minimizing the area under the time-concentration curve (AUC), which is equivalent to minimizing the cumulative dosage. We first solve this problem under the assumption that an arbitrary antimicrobial concentration profile may be chosen, and prove that the ideal concentration profile consists of a constant concentration over a finite time duration, where explicit expressions for the optimal concentration and the time duration are given in terms of the pharmacodynamic parameters. Since antimicrobial concentration profiles are induced by a dosing schedule and the antimicrobial pharmacokinetics, the 'ideal' concentration profile is not strictly feasible. We therefore also investigate the possibility of achieving outcomes which are close to those provided by the 'ideal' concentration profile, using a bolus+continuous dosing schedule, which consists of a loading dose followed by infusion of the antimicrobial at a constant rate. We explicitly find the optimal bolus+continuous dosing schedule, and show that, for realistic parameter ranges, this schedule achieves results which are nearly as efficient as those attained by the 'ideal' concentration profile. The optimality results obtained here provide a baseline and reference point for comparison and evaluation of antimicrobial treatment plans.

Rapid In Vitro Assessment of Antimicrobial Drug Effect Bridging Clinically Relevant Pharmacokinetics: A Comprehensive Methodology

Rapid in vitro assessment of antimicrobial drug efficacy under clinically relevant pharmacokinetic conditions is an essential element of both drug development and clinical use. Here, we present a comprehensive overview of a recently developed novel integrated methodology for rapid assessment of such efficacy, particularly against the emergence of resistant bacterial strains, as jointly researched by the authors in recent years. This methodology enables rapid in vitro assessment of the antimicrobial efficacy of single or multiple drugs in combination, following clinically relevant pharmacokinetics. The proposed methodology entails (a) the automated collection of longitudinal time-kill data in an optical-density instrument; (b) the processing of collected time-kill data with the aid of a mathematical model to determine optimal dosing regimens under clinically relevant pharmacokinetics for single or multiple drugs; and (c) in vitro validation of promising dosing regimens in a hollow fiber system. Proof-of-concept of this methodology through a number of in vitro studies is discussed. Future directions for the refinement of optimal data collection and processing are discussed.

A survey of within-host and between-hosts modelling for antibiotic resistance

Antibiotic resistance is a global public health problem which has the attention of many stakeholders including clinicians, the pharmaceutical industry, researchers and policy makers. Despite the existence of many studies, control of resistance transmission has become a rather daunting task as the mechanisms underlying resistance evolution and development are not fully known. Here, we discuss the mechanisms underlying antibiotic resistance development, explore some treatment strategies used in the fight against antibiotic resistance and consider recent findings on collateral susceptibilities amongst antibiotic classes. Mathematical models have proved valuable for unravelling complex mechanisms in biology and such models have been used in the quest of understanding the development and spread of antibiotic resistance. While assessing the importance of such mathematical models, previous systematic reviews were interested in investigating whether these models follow good modelling practice. We focus on theoretical approaches used for resistance modelling considering both within and between host models as well as some pharmacodynamic and pharmakokinetic approaches and further examine the interaction between drugs and host immune response during treatment with antibiotics. Finally, we provide an outlook for future research aimed at modelling approaches for combating antibiotic resistance.

Send more data: a systematic review of mathematical models of antimicrobial resistance

Background

Antimicrobial resistance is a global health problem that demands all possible means to control it. Mathematical modelling is a valuable tool for understanding the mechanisms of AMR development and spread, and can help us to investigate and propose novel control strategies. However, it is of vital importance that mathematical models have a broad utility, which can be assured if good modelling practice is followed.

Objective

The objective of this study was to provide a comprehensive systematic review of published models of AMR development and spread. Furthermore, the study aimed to identify gaps in the knowledge required to develop useful models.

Methods

The review comprised a comprehensive literature search with 38 selected studies. Information was extracted from the selected papers using an adaptation of previously published frameworks, and was evaluated using the TRACE good modelling practice guidelines.

Results

None of the selected papers fulfilled the TRACE guidelines. We recommend that future mathematical models should: a) model the biological processes mechanistically, b) incorporate uncertainty and variability in the system using stochastic modelling, c) include a sensitivity analysis and model external and internal validation.

Conclusion

Many mathematical models of AMR development and spread exist. There is still a lack of knowledge about antimicrobial resistance, which restricts the development of useful mathematical models.