Mathematical modelling of bacterial resistance to multiple antibiotics and immune system response

Sub-inhibitory antibiotic treatment selects for enhanced metabolic efficiency

Bacterial growth and metabolic rates are often closely related. However, under antibiotic selection, a paradox in this relationship arises: antibiotic efficacy decreases when bacteria are metabolically dormant, yet antibiotics select for resistant cells that grow fastest during treatment. That is, antibiotic selection counterintuitively favors bacteria with fast growth but slow metabolism. Despite this apparent contradiction, antibiotic resistant cells have historically been characterized primarily in the context of growth, whereas the extent of analogous changes in metabolism is comparatively unknown. Here, we observed that previously evolved antibiotic-resistant strains exhibited a unique relationship between growth and metabolism whereby nutrient utilization became more efficient, regardless of the growth rate. To better understand this unexpected phenomenon, we used a simplified model to simulate bacterial populations adapting to sub-inhibitory antibiotic selection through successive bottlenecking events. Simulations predicted that sub-inhibitory bactericidal antibiotic concentrations could select for enhanced metabolic efficiency, defined based on nutrient utilization: drug-adapted cells are able to achieve the same biomass while utilizing less substrate, even in the absence of treatment. Moreover, simulations predicted that restoring metabolic efficiency would re-sensitize resistant bacteria exhibiting metabolic-dependent resistance; we confirmed this result using adaptive laboratory evolutions of Escherichia coli under carbenicillin treatment. Overall, these results indicate that metabolic efficiency is under direct selective pressure during antibiotic treatment and that differences in evolutionary context may determine both the efficacy of different antibiotics and corresponding re-sensitization approaches.IMPORTANCEThe sustained emergence of antibiotic-resistant pathogens combined with the stalled drug discovery pipelines highlights the critical need to better understand the underlying evolution mechanisms of antibiotic resistance. To this end, bacterial growth and metabolic rates are often closely related, and resistant cells have historically been characterized exclusively in the context of growth. However, under antibiotic selection, antibiotics counterintuitively favor cells with fast growth, and slow metabolism. Through an integrated approach of mathematical modeling and experiments, this study thereby addresses the significant knowledge gap of whether antibiotic selection drives changes in metabolism that complement, and/or act independently, of antibiotic resistance phenotypes.

Dynamic analysis of a bacterial resistance model with impulsive state feedback control

Bacterial resistance caused by prolonged administration of the same antibiotics exacerbates the threat of bacterial infection to human health. It is essential to optimize antibiotic treatment measures. In this paper, we formulate a simplified model of conversion between sensitive and resistant bacteria. Subsequently, impulsive state feedback control is introduced to reduce bacterial resistance to a low level. The global asymptotic stability of the positive equilibrium and the orbital stability of the order-1 periodic solution are proved by the Poincaré-Bendixson Theorem and the theory of the semi-continuous dynamical system, respectively. Finally, numerical simulations are performed to validate the accuracy of the theoretical findings.

Identification of the elements of models of antimicrobial resistance of bacteria for assessing their usefulness and usability in One Health decision making: a protocol for scoping review

INTRODUCTION

Antimicrobial resistance (AMR) is a complex problem that requires the One Health approach, that is, a collaboration among various disciplines working in different sectors (animal, human and environment) to resolve it. Mathematical and statistical models have been used to understand AMR development, emergence, dissemination, prediction and forecasting. A review of the published models of AMR will help consolidate our knowledge of the dynamics of AMR and will also facilitate decision-makers and researchers in evaluating the credibility, generalisability and interpretation of the results and aspects of AMR models. The study objective is to identify and synthesise knowledge on mathematical and statistical models of AMR among bacteria in animals, humans and environmental compartments.

METHODS AND ANALYSIS

Eligibility criteria: Original research studies reporting mathematical and statistical models of AMR among bacteria in animal, human and environmental compartments that were published until 2022 in English, French and Spanish will be included in this study.

SOURCES OF EVIDENCE

Database of PubMed, Agricola (Ovid), Centre for Agriculture and Bioscience Direct (CABI), Web of Science (Clarivate), Cumulative Index to Nursing and Allied Health Literature (CINAHL) and MathScinet. Data charting: Metadata of the study, the context of the study, model structure, model process and reporting quality will be extracted. A narrative summary of this information, gaps and recommendations will be prepared and reported in One Health decision-making context.

ETHICS AND DISSEMINATION

Research ethics board approval was not obtained for this study as neither human participation nor unpublished human data were used in this study. The study findings will be widely disseminated among the One Health Modelling Network for Emerging Infections network and stakeholders by means of conferences, and publication in open-access peer-reviewed journals.

Stability analysis of the hiv model through incommensurate fractional-order nonlinear system

In this study, it is employed a new model of HIV infection in the form of incommensurate fractional differential equations systems involving the Caputo fractional derivative. Existence of the model's equilibrium points has been investigated. According to some special cases of the derivative-orders in the proposed model, the asymptotic stability of the infection-free equilibrium and endemic equilibrium has been proved under certain conditions. These stability conditions related to the derivative-orders depend on not only the basic reproduction rate frequently emphasized in the literature but also the newly obtained conditions in this study. Qualitative analysis results were complemented by numerical simulations in Matlab, illustrating the obtained stability result.

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.

Computational Health Engineering Applied to Model Infectious Diseases and Antimicrobial Resistance Spread

Infectious diseases are the primary cause of mortality worldwide. The dangers of infectious disease are compounded with antimicrobial resistance, which remains the greatest concern for human health. Although novel approaches are under investigation, the World Health Organization predicts that by 2050, septicaemia caused by antimicrobial resistant bacteria could result in 10 million deaths per year. One of the main challenges in medical microbiology is to develop novel experimental approaches, which enable a better understanding of bacterial infections and antimicrobial resistance. After the introduction of whole genome sequencing, there was a great improvement in bacterial detection and identification, which also enabled the characterization of virulence factors and antimicrobial resistance genes. Today, the use of in silico experiments jointly with computational and machine learning offer an in depth understanding of systems biology, allowing us to use this knowledge for the prevention, prediction, and control of infectious disease. Herein, the aim of this review is to discuss the latest advances in human health engineering and their applicability in the control of infectious diseases. An in-depth knowledge of host–pathogen–protein interactions, combined with a better understanding of a host’s immune response and bacterial fitness, are key determinants for halting infectious diseases and antimicrobial resistance dissemination.

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.

Antibiotic-driven escape of host in a parasite-induced Red Queen dynamics

Winnerless coevolution of hosts and parasites could exhibit Red Queen dynamics, which is characterized by parasite-driven cyclic switching of expressed host phenotypes. We hypothesize that the application of antibiotics to suppress the reproduction of parasites can provide an opportunity for the hosts to escape such winnerless coevolution. Here, we formulate a minimal mathematical model of host-parasite interaction involving multiple host phenotypes that are targeted by adapting parasites. Our model predicts the levels of antibiotic effectiveness that can steer the parasite-driven cyclic switching of host phenotypes (oscillations) to a stable equilibrium of host survival. Our simulations show that uninterrupted application of antibiotic with high-level effectiveness (greater than 85%) is needed to escape the Red Queen dynamics. Interrupted and low level of antibiotic effectiveness are indeed useless to stop host-parasite coevolution. This study can be a guide in designing good practices and protocols to minimize the risk of further progression of parasitic infections.