A modeling framework for the evolution and spread of antibiotic resistance: literature review and model categorization

Modeling the transmission of antibiotic-resistant Enterobacterales in the community: A systematic review

BACKGROUND

Antibiotic-resistant Enterobacterales (ARE) are a public health threat worldwide. Dissemination of these opportunistic pathogens has been largely studied in hospitals. Despite high prevalence of asymptomatic colonization in the community in some regions of the world, less is known about ARE acquisition and spread in this setting. As explaining the community ARE dynamics has not been straightforward, mathematical models can be key to explore underlying phenomena and further evaluate the impact of interventions to curb ARE circulation outside of hospitals.

METHODS

We conducted a systematic review of mathematical modeling studies focusing on the transmission of AR-E in the community, excluding models only specific to hospitals. We extracted model features (population, setting), formalism (compartmental, individual-based), biological hypotheses (transmission, infection, antibiotic impact, resistant strain specificities) and main findings. We discussed additional mechanisms to be considered, open scientific questions, and most pressing data needs.

RESULTS

We identified 18 modeling studies focusing on the human transmission of ARE in the community (n=11) or in both community and hospital (n=7). Models aimed at (i) understanding mechanisms driving resistance dynamics; (ii) identifying and quantifying transmission routes; or (iii) evaluating public health interventions to reduce resistance. To overcome the difficulty of reproducing observed ARE dynamics in the community using the classical two-strains competition model, studies proposed to include mechanisms such as within-host strain competition or a strong host population structure. Studies inferring model parameters from longitudinal carriage data were mostly based on models considering the ARE strain only. They showed differences in ARE carriage duration depending on the acquisition mode: returning travelers have a significantly shorter carriage duration than discharged hospitalized patient or healthy individuals. Interestingly, predictions across models regarding the success of public health interventions to reduce ARE rates depended on pathogens, settings, and antibiotic resistance mechanisms. For E. coli, reducing person-to-person transmission in the community had a stronger effect than reducing antibiotic use in the community. For Klebsiella pneumoniae, reducing antibiotic use in hospitals was more efficient than reducing community use.

CONCLUSIONS

This study raises the limited number of modeling studies specifically addressing the transmission of ARE in the community. It highlights the need for model development and community-based data collection especially in low- and middle-income countries to better understand acquisition routes and their relative contribution to observed ARE levels. Such modeling will be critical to correctly design and evaluate public health interventions to control ARE transmission in the community and further reduce the associated infection burden.

Cefiderocol for treating severe aerobic Gram-negative bacterial infections: technology evaluation to inform a novel subscription-style payment model

Background

To limit the use of antimicrobials without disincentivising the development of novel antimicrobials, there is interest in establishing innovative models that fund antimicrobials based on an evaluation of their value as opposed to the volumes used. The aim of this project was to evaluate the population-level health benefit of cefiderocol in the NHS in England, for the treatment of severe aerobic Gram-negative bacterial infections when used within its licensed indications. The results were used to inform the National Institute for Health and Care Excellence guidance in support of commercial discussions regarding contract value between the manufacturer and NHS England.

Methods

The health benefit of cefiderocol was first derived for a series of high-value clinical scenarios. These represented uses that were expected to have a significant impact on patients' mortality risks and health-related quality of life. The clinical effectiveness of cefiderocol relative to its comparators was estimated by synthesising evidence on susceptibility of the pathogens of interest to the antimicrobials in a network meta-analysis. Patient-level costs and health outcomes of cefiderocol under various usage scenarios compared with alternative management strategies were quantified using decision modelling. Results were reported as incremental net health effects expressed in quality-adjusted life-years, which were scaled to 20-year population values using infection number forecasts based on data from Public Health England. The outcomes estimated for the high-value clinical scenarios were extrapolated to other expected uses for cefiderocol.

Results

Among Enterobacterales isolates with the metallo-beta-lactamase resistance mechanism, the base-case network meta-analysis found that cefiderocol was associated with a lower susceptibility relative to colistin (odds ratio 0.32, 95% credible intervals 0.04 to 2.47), but the result was not statistically significant. The other treatments were also associated with lower susceptibility than colistin, but the results were not statistically significant. In the metallo-beta-lactamase Pseudomonas aeruginosa base-case network meta-analysis, cefiderocol was associated with a lower susceptibility relative to colistin (odds ratio 0.44, 95% credible intervals 0.03 to 3.94), but the result was not statistically significant. The other treatments were associated with no susceptibility. In the base case, patient-level benefit of cefiderocol was between 0.02 and 0.15 quality-adjusted life-years, depending on the site of infection, the pathogen and the usage scenario. There was a high degree of uncertainty surrounding the benefits of cefiderocol across all subgroups. There was substantial uncertainty in the number of infections that are suitable for treatment with cefiderocol, so population-level results are presented for a range of scenarios for the current infection numbers, the expected increases in infections over time and rates of emergence of resistance. The population-level benefits varied substantially across the base-case scenarios, from 896 to 3559 quality-adjusted life-years over 20 years.

Conclusion

This work has provided quantitative estimates of the value of cefiderocol within its areas of expected usage within the NHS.

Limitations

Given existing evidence, the estimates of the value of cefiderocol are highly uncertain.

Future work

Future evaluations of antimicrobials would benefit from improvements to NHS data linkages; research to support appropriate synthesis of susceptibility studies; and application of routine data and decision modelling to assess enablement value.

Study registration

No registration of this study was undertaken.

Funding

This award was funded by the National Institute for Health and Care Research (NIHR) Health Technology Assessment Policy Research Programme (NIHR award ref: NIHR135591), conducted through the Policy Research Unit in Economic Methods of Evaluation in Health and Social Care Interventions, PR-PRU-1217-20401, and is published in full in Health Technology Assessment; Vol. 28, No. 28. See the NIHR Funding and Awards website for further award information.

Mathematical models of drug-resistant tuberculosis lack bacterial heterogeneity: A systematic review

Drug-resistant tuberculosis (DR-TB) threatens progress in the control of TB. Mathematical models are increasingly being used to guide public health decisions on managing both antimicrobial resistance (AMR) and TB. It is important to consider bacterial heterogeneity in models as it can have consequences for predictions of resistance prevalence, which may affect decision-making. We conducted a systematic review of published mathematical models to determine the modelling landscape and to explore methods for including bacterial heterogeneity. Our first objective was to identify and analyse the general characteristics of mathematical models of DR-mycobacteria, including M. tuberculosis. The second objective was to analyse methods of including bacterial heterogeneity in these models. We had different definitions of heterogeneity depending on the model level. For between-host models of mycobacterium, heterogeneity was defined as any model where bacteria of the same resistance level were further differentiated. For bacterial population models, heterogeneity was defined as having multiple distinct resistant populations. The search was conducted following PRISMA guidelines in five databases, with studies included if they were mechanistic or simulation models of DR-mycobacteria. We identified 195 studies modelling DR-mycobacteria, with most being dynamic transmission models of non-treatment intervention impact in M. tuberculosis (n = 58). Studies were set in a limited number of specific countries, and 44% of models (n = 85) included only a single level of "multidrug-resistance (MDR)". Only 23 models (8 between-host) included any bacterial heterogeneity. Most of these also captured multiple antibiotic-resistant classes (n = 17), but six models included heterogeneity in bacterial populations resistant to a single antibiotic. Heterogeneity was usually represented by different fitness values for bacteria resistant to the same antibiotic (61%, n = 14). A large and growing body of mathematical models of DR-mycobacterium is being used to explore intervention impact to support policy as well as theoretical explorations of resistance dynamics. However, the majority lack bacterial heterogeneity, suggesting that important evolutionary effects may be missed.

Fate and transport modelling for evaluating antibiotic resistance in aquatic environments: Current knowledge and research priorities

Antibiotics have revolutionised medicine in the last century and enabled the prevention of bacterial infections that were previously deemed untreatable. However, in parallel, bacteria have increasingly developed resistance to antibiotics through various mechanisms. When resistant bacteria find their way into terrestrial and aquatic environments, animal and human exposures increase, e.g., via polluted soil, food, and water, and health risks multiply. Understanding the fate and transport of antibiotic resistant bacteria (ARB) and the transfer mechanisms of antibiotic resistance genes (ARGs) in aquatic environments is critical for evaluating and mitigating the risks of resistant-induced infections. The conceptual understanding of sources and pathways of antibiotics, ARB, and ARGs from society to the water environments is essential for setting the scene and developing an appropriate framework for modelling. Various factors and processes associated with hydrology, ecology, and climate change can significantly affect the fate and transport of ARB and ARGs in natural environments. This article reviews current knowledge, research gaps, and priorities for developing water quality models to assess the fate and transport of ARB and ARGs. The paper also provides inputs on future research needs, especially the need for new predictive models to guide risk assessment on AR transmission and spread in aquatic environments.

Modelling the effects of antibiotic usage in livestock on human salmonellosis

Antibiotic usage in livestock has been suggested as a driver of antimicrobial resistance in human and livestock populations. This has contributed to the implementation of stewardship programs to curtail usage of antibiotics in livestock. However, the consequences of antibiotic curtailment in livestock on human health are poorly understood. There is the potential for increases in the carriage of pathogens such as Salmonella spp. in livestock, and subsequent increases in human foodborne disease. We use a mathematical model fitted to four case studies, ampicillin and tetracycline usage in fattening pig and broiler poultry populations, to explore the impact of curtailing antibiotic usage in livestock on salmonellosis in humans. Increases in the daily incidence of salmonellosis and a decrease in the proportion of resistant salmonellosis were identified following curtailment of antibiotic usage in livestock. The extent of these increases in human foodborne disease ranged from negligible, to controllable through interventions to target the farm-to-fork pathway. This study provides a motivating example of one plausible scenario following curtailment of antibiotic usage in livestock and suggests that a focus on ensuring good farm-to-fork hygiene and livestock biosecurity is sufficient to mitigate the negative human health consequences of antibiotic stewardship in livestock populations.

Taxation of veterinary antibiotics to reduce antimicrobial resistance

Routine usage of antibiotics for animal health is a key driver of antimicrobial resistance (AMR) in food-producing animals. Taxation is a possible approach to incentivise appropriate antibiotic usage in food-producing animals. Taxation can be applied flatly across all antibiotic classes, targeted to single antibiotic classes, or scaled based on resistance in each class, so called "differential" taxation. However, quantifying the potential impact of taxation is challenging, due to the nonlinear and unintuitive response of AMR dynamics to interventions and changes in antibiotic usage caused by alterations in price. We combine epidemiological models with price elasticities of demand for veterinary antibiotics, to compare the potential benefits of taxation schemes with currently implemented bans on antibiotic usage. Taxation strategies had effects comparable to bans on antibiotic usage in food-producing animals to reduce average resistance prevalence and prevent increases in overall infection. Taxation could also maximise the average number of antibiotics with a resistance prevalence of under 25% and potentially generate annual global revenues of ∼1 billion US$ under a 50% taxation to current prices of food-producing animal antibiotics. Differential taxation was also able to maintain a high availability of antibiotics over time compared to single and flat taxation strategies, while also having the lowest rates of intervention failure and highest potential revenue across all taxation strategies. These findings suggest that taxation should be further explored as a tool to combat the ongoing AMR crisis.

Impact of Technological Developments on Infectious Disease Epidemiology: Lessons From the First 100 Years of the American Journal of Epidemiology

Technological developments in laboratory and epidemiologic methods, combined with increasing computing power, have synergistically increased our understanding of the epidemiology of infectious disease. Using historical examples from the first 100 years of the American Journal of Epidemiology, we illustrate how these developments provided the foundation for the rapid detection of the agent causing coronavirus disease 2019 (COVID-19), severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), from its transmission efficiency and modalities, risk factors, and natural history to the evaluation of new vaccines and treatments to control its spread and impact. Comparisons with timelines for elucidation of the epidemiology, natural history, and control of other infectious diseases, including viral hepatitis, humbly remind us of how much past discoveries have paved the way for more rapid discovery of and response to new pathogens. We close with some comments on a potential future role of the Journal in infectious disease epidemiology.

Modelling antimicrobial resistance transmission to guide personalized antimicrobial stewardship interventions and infection control policies in healthcare setting: a pilot study

Infection control programs and antimicrobial stewardship have been proven effective in reducing the burden of diseases due to multidrug-resistant organisms, but quantifying the effect of each intervention is an open issue. For this aim, we propose a model to characterize the effect of interventions at single ward level. We adapted the Ross-Macdonald model to describe hospital cross-transmission dynamics of carbapenem resistant Klebsiella pneumoniae (CRKP), considering healthcare workers as the vectors transmitting susceptible and resistant pathogens among admitted patients. The model parameters were estimated from a literature review, further adjusted to reproduce observed clinical outcomes, and validated using real life data from a 2-year study in a university hospital. The model has been further explored through extensive sensitivity analysis, in order to assess the relevance of single interventions as well as their synergistic effects. Our model has been shown to be an effective tool to describe and predict the impact of interventions in reducing the prevalence of CRKP colonisation and infection, and can be extended to other specific hospital and pathological scenarios to produce tailored estimates of the most effective strategies.

Estimating the fitness cost and benefit of antimicrobial resistance from pathogen genomic data

Increasing levels of antibiotic resistance in many bacterial pathogen populations are a major threat to public health. Resistance to an antibiotic provides a fitness benefit when the bacteria are exposed to this antibiotic, but resistance also often comes at a cost to the resistant pathogen relative to susceptible counterparts. We lack a good understanding of these benefits and costs of resistance for many bacterial pathogens and antibiotics, but estimating them could lead to better use of antibiotics in a way that reduces or prevents the spread of resistance. Here, we propose a new model for the joint epidemiology of susceptible and resistant variants, which includes explicit parameters for the cost and benefit of resistance. We show how Bayesian inference can be performed under this model using phylogenetic data from susceptible and resistant lineages and that by combining data from both we are able to disentangle and estimate the resistance cost and benefit parameters separately. We applied our inferential methodology to several simulated datasets to demonstrate good scalability and accuracy. We analysed a dataset of Neisseria gonorrhoeae genomes collected between 2000 and 2013 in the USA. We found that two unrelated lineages resistant to fluoroquinolones shared similar epidemic dynamics and resistance parameters. Fluoroquinolones were abandoned for the treatment of gonorrhoea due to increasing levels of resistance, but our results suggest that they could be used to treat a minority of around 10% of cases without causing resistance to grow again.

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.

Ecology, more than antibiotics consumption, is the major predictor for the global distribution of aminoglycoside-modifying enzymes

Antibiotic consumption and its abuses have been historically and repeatedly pointed out as the major driver of antibiotic resistance emergence and propagation. However, several examples show that resistance may persist despite substantial reductions in antibiotic use, and that other factors are at stake. Here, we study the temporal, spatial, and ecological distribution patterns of aminoglycoside resistance, by screening more than 160,000 publicly available genomes for 27 clusters of genes encoding aminoglycoside-modifying enzymes (AME genes). We find that AME genes display a very ubiquitous pattern: about 25% of sequenced bacteria carry AME genes. These bacteria were sequenced from all the continents (except Antarctica) and terrestrial biomes, and belong to a wide number of phyla. By focusing on European countries between 1997 and 2018, we show that aminoglycoside consumption has little impact on the prevalence of AME-gene-carrying bacteria, whereas most variation in prevalence is observed among biomes. We further analyze the resemblance of resistome compositions across biomes: soil, wildlife, and human samples appear to be central to understand the exchanges of AME genes between different ecological contexts. Together, these results support the idea that interventional strategies based on reducing antibiotic use should be complemented by a stronger control of exchanges, especially between ecosystems.

Check your assumptions: Further scrutiny of basic model frameworks of antimicrobial resistance

Since the mid-1990s, growing concerns over antimicrobial resistant (AMR) organisms has led to an increase in the use of mathematical models to explore the inter-host transmission of such infections. Previous work reviewing such models categorised them into generic frameworks based on their underlying assumptions. These assumptions dictated the coexistence between AMR and antimicrobial sensitive strains. We add to this work performing stability analyses of the frameworks, along with simulating them deterministically and stochastically. Stability analyses found that many of these assumptions lead to models having the same equilibria, but showed differences in the equilibria's stability between models. Deterministic simulations reveal that assuming replacement of one infecting strain by another leads to an unusual antimicrobial treatment threshold. Increasing beyond this threshold causes a discontinuous increase in disease burden. The cost of AMR to pathogen fitness (lowered transmission) dictates both the threshold of treatment that causes the discontinuous increase in disease burden and the size of that increase. It was also shown that Superinfection states can be biased against resident strains and so favour coexistence of both strains. Stochastic simulations demonstrated that differing scenario starting conditions can guide models to converge upon equilibria that they may not have under deterministic simulation. These findings highlight the importance of checking assumptions when modelling AMR and strain competition more widely.

Modelling the Future Clinical and Economic Burden of Antimicrobial Resistance: The Feasibility and Value of Models to Inform Policy

Due to the increasing threat to public health and the economy, governments internationally are interested in models to estimate the future clinical and economic burden of antimicrobial resistance (AMR) and to evaluate the cost-effectiveness of interventions to prevent or control resistance and to inform resource-allocation decision making. A widely cited UK report estimated that 10 million additional deaths will occur globally per annum due to AMR by 2050; however, the utility and accuracy of this prediction has been challenged. The precision of models predicting the future economic burden of AMR is dependent upon the accuracy of predicting future resistance rates. This paper reviews the feasibility and value of modelling to inform policy and resource allocation to manage and curb AMR. Here we describe methods used to estimate future resistance in published burden-of-disease models; the sources of uncertainty are highlighted, which could potentially mislead policy decision-making. While broad assumptions can be made regarding some predictable factors contributing to future resistance rates, the unexpected emergence, establishment and spread of new resistance genes introduces substantial uncertainty into estimates of future economic burden, and in models evaluating the effectiveness of interventions or policies to address AMR. Existing reporting standards for best practice in modelling should be adapted to guide the reporting of AMR economic models, to ensure model transparency and validation for interpretation by policymakers.

ASAS-NANP symposium: mathematical modeling in animal nutrition: the progression of data analytics and artificial intelligence in support of sustainable development in animal science

A renewed interest in data analytics and decision support systems in developing automated computer systems is facilitating the emergence of hybrid intelligent systems by combining artificial intelligence (AI) algorithms with classical modeling paradigms such as mechanistic modeling (HIMM) and agent-based models (iABM). Data analytics have evolved remarkably, and the scientific community may not yet fully grasp the power and limitations of some tools. Existing statistical assumptions might need to be re-assessed to provide a more thorough competitive advantage in animal production systems towards sustainability. This paper discussed the evolution of data analytics from a competitive advantage perspective within academia and illustrated the combination of different advanced technological systems in developing HIMM. The progress of analytical tools was divided into three stages: collect and respond, predict and prescribe, and smart learning and policy making, depending on the level of their sophistication (simple to complicated analysis). The collect and respond stage is responsible for ensuring the data is correct and free of influential data points, and it represents the data and information phases for which data are cataloged and organized. The predict and prescribe stage results in gained knowledge from the data and comprises most predictive modeling paradigms, and optimization and risk assessment tools are used to prescribe future decision-making opportunities. The third stage aims to apply the information obtained in the previous stages to foment knowledge and use it for rational decisions. This stage represents the pinnacle of acquired knowledge that leads to wisdom, and AI technology is intrinsic. Although still incipient, HIMM and iABM form the forthcoming stage of competitive advantage. HIMM may not increase our ability to understand the underlying mechanisms controlling the outcomes of a system, but it may increase the predictive ability of existing models by helping the analyst explain more of the data variation. The scientific community still has some issues to be resolved, including the lack of transparency and reporting of AI that might limit code reproducibility. It might be prudent for the scientific community to avoid the shiny object syndrome (i.e., AI) and look beyond the current knowledge to understand the mechanisms that might improve productivity and efficiency to lead agriculture towards sustainable and responsible achievements.

A Review on Occurrence and Spread of Antibiotic Resistance in Wastewaters and in Wastewater Treatment Plants: Mechanisms and Perspectives

This paper reviews current knowledge on sources, spread and removal mechanisms of antibiotic resistance genes (ARGs) in microbial communities of wastewaters, treatment plants and downstream recipients. Antibiotic is the most important tool to cure bacterial infections in humans and animals. The over- and misuse of antibiotics have played a major role in the development, spread, and prevalence of antibiotic resistance (AR) in the microbiomes of humans and animals, and microbial ecosystems worldwide. AR can be transferred and spread amongst bacteria via intra- and interspecies horizontal gene transfer (HGT). Wastewater treatment plants (WWTPs) receive wastewater containing an enormous variety of pollutants, including antibiotics, and chemicals from different sources. They contain large and diverse communities of microorganisms and provide a favorable environment for the spread and reproduction of AR. Existing WWTPs are not designed to remove micropollutants, antibiotic resistant bacteria (ARB) and ARGs, which therefore remain present in the effluent. Studies have shown that raw and treated wastewaters carry a higher amount of ARB in comparison to surface water, and such reports have led to further studies on more advanced treatment processes. This review summarizes what is known about AR removal efficiencies of different wastewater treatment methods, and it shows the variations among different methods. Results vary, but the trend is that conventional activated sludge treatment, with aerobic and/or anaerobic reactors alone or in series, followed by advanced post treatment methods like UV, ozonation, and oxidation removes considerably more ARGs and ARB than activated sludge treatment alone. In addition to AR levels in treated wastewater, it examines AR levels in biosolids, settled by-product from wastewater treatment, and discusses AR removal efficiency of different biosolids treatment procedures. Finally, it puts forward key-points and suggestions for dealing with and preventing further increase of AR in WWTPs and other aquatic environments, together with a discussion on the use of mathematical models to quantify and simulate the spread of ARGs in WWTPs. Mathematical models already play a role in the analysis and development of WWTPs, but they do not consider AR and challenges remain before models can be used to reliably study the dynamics and reduction of AR in such systems.

Microbiome-pathogen interactions drive epidemiological dynamics of antibiotic resistance: A modeling study applied to nosocomial pathogen control

The human microbiome can protect against colonization with pathogenic antibiotic-resistant bacteria (ARB), but its impacts on the spread of antibiotic resistance are poorly understood. We propose a mathematical modeling framework for ARB epidemiology formalizing within-host ARB-microbiome competition, and impacts of antibiotic consumption on microbiome function. Applied to the healthcare setting, we demonstrate a trade-off whereby antibiotics simultaneously clear bacterial pathogens and increase host susceptibility to their colonization, and compare this framework with a traditional strain-based approach. At the population level, microbiome interactions drive ARB incidence, but not resistance rates, reflecting distinct epidemiological relevance of different forces of competition. Simulating a range of public health interventions (contact precautions, antibiotic stewardship, microbiome recovery therapy) and pathogens (Clostridioides difficile, methicillin-resistant Staphylococcus aureus, multidrug-resistant Enterobacteriaceae) highlights how species-specific within-host ecological interactions drive intervention efficacy. We find limited impact of contact precautions for Enterobacteriaceae prevention, and a promising role for microbiome-targeted interventions to limit ARB spread.

Antibiotic treatment protocols revisited: the challenges of a conclusive assessment by mathematical modelling

Hospital-acquired bacterial infections lead to prolonged hospital stays and increased mortality. The problem is exacerbated by antibiotic-resistant strains that delay or impede effective treatment. To ensure successful therapy and to manage antibiotic resistance, treatment protocols that draw on several different antibiotics might be used. This includes the administration of drug cocktails to individual patients (combination therapy) but also the random assignment of drugs to different patients (mixing) and a regular switch in the default drug used in the hospital from drug A to drug B and back (cycling). For more than 20 years, mathematical models have been used to assess the prospects of antibiotic combination therapy, mixing and cycling. But while tendencies in their ranking across studies have emerged, the picture remains surprisingly inconclusive and incomplete. In this article, we review existing modelling studies and demonstrate by means of examples how methodological factors complicate the emergence of a consistent picture. These factors include the choice of the criterion by which the effects of the protocols are compared, the model implementation and its analysis. We thereafter discuss how progress can be made and suggest future modelling directions.

Optimal dynamic empirical therapy in a health care facility: A Monte-Carlo look-ahead method

BACKGROUND AND OBJECTIVES

Empirical antimicrobial prescription strategies have been proposed to counteract the selection of resistant pathogenic strains. The respective merits of such strategies have been debated. Rather than comparing a finite number of policies, we take an optimization approach and propose a solution to the problem of finding an empirical therapy policy in a health care facility that minimizes the cumulative infected patient-days over a given time horizon.

METHODS

We assume that the parameters of the model are known and that when the policy is implemented, all patients receive the same treatment at a given time. We model the emergence and spread of antimicrobial resistance at the population level with the stochastic version of a compartmental model. The model features two drugs and the possibility of double resistance. Our solution method is a rollout algorithm.

RESULTS

In our example, the optimal policy computed with this method allows to reduce the average cumulative infected patient-days over two years by 22% compared to the best standard therapy. Considering regularity constraints, we could derive a policy with a fixed period and a performance close to that of the optimal policy. The average cumulative infected patient-days over two years obtained with the optimal policy is 6% lower (significantly at the 95% threshold) than that obtained with the fixed period policy.

CONCLUSION

Our results illustrate the performance of a highly flexible solution method that will contribute to the development of implementable empirical therapy policies.

Treating symptomatic infections and the co-evolution of virulence and drug resistance

Antimicrobial therapeutic treatments are by definition applied after the onset of symptoms, which tend to correlate with infection severity. Using mathematical epidemiology models, I explore how this link affects the coevolutionary dynamics between the virulence of an infection, measured via host mortality rate, and its susceptibility to chemotherapy. I show that unless resistance pre-exists in the population, drug-resistant infections are initially more virulent than drug-sensitive ones. As the epidemic unfolds, virulence is more counter-selected in drug-sensitive than in drug-resistant infections. This difference decreases over time and, eventually, the exact shape of genetic trade-offs govern long-term evolutionary dynamics. Using adaptive dynamics, I show that two types of evolutionary stable strategies (ESS) may be reached in the context of this simple model and that, depending on the parameter values, an ESS may only be locally stable. In general, the more the treatment rate increases with virulence, the lower the ESS value. Overall, both on the short-term and long-term, having treatment rate depend on infection virulence tend to favour less virulent strains in drug-sensitive infections. These results highlight the importance of the feedbacks between epidemiology, public health policies and parasite evolution, and have implications for the monitoring of virulence evolution.

Modeling transport of antibiotic resistant bacteria in aquatic environment using stochastic differential equations

Contaminated sites are recognized as the "hotspot" for the development and spread of antibiotic resistance in environmental bacteria. It is very challenging to understand mechanism of development of antibiotic resistance in polluted environment in the presence of different anthropogenic pollutants. Uncertainties in the environmental processes adds complexity to the development of resistance. This study attempts to develop mathematical model by using stochastic partial differential equations for the transport of fluoroquinolone and its resistant bacteria in riverine environment. Poisson's process is assumed for the diffusion approximation in the stochastic partial differential equations (SPDE). Sensitive analysis is performed to evaluate the parameters and variables for their influence over the model outcome. Based on their sensitivity, the model parameters and variables are chosen and classified into environmental, demographic, and anthropogenic categories to investigate the sources of stochasticity. Stochastic partial differential equations are formulated for the state variables in the model. This SPDE model is then applied to the 100 km stretch of river Musi (South India) and simulations are carried out to assess the impact of stochasticity in model variables on the resistant bacteria population in sediments. By employing the stochasticity in model variables and parameters we came to know that environmental and anthropogenic variations are not able to affect the resistance dynamics at all. Demographic variations are able to affect the distribution of resistant bacteria population uniformly with standard deviation between 0.087 and 0.084, however, is not significant to have any biological relevance to it. The outcome of the present study is helpful in simplifying the model for practical applications. This study is an ongoing effort to improve the model for the transport of antibiotics and transport of antibiotic resistant bacteria in polluted river. There is a wide gap between the knowledge of stochastic resistant bacterial growth dynamics and the knowledge of transport of antibiotic resistance in polluted aquatic environment, this study is one step towards filling up that gap.

Predicting the future distribution of antibiotic resistance using time series forecasting and geospatial modelling

Background: Increasing antibiotic resistance in a location may be mitigated by changes in treatment policy, or interventions to limit transmission of resistant bacteria. Therefore, accurate forecasting of the distribution of antibiotic resistance could be advantageous. Two previously published studies addressed this, but neither study compared alternative forecasting algorithms or considered spatial patterns of resistance spread. Methods: We analysed data describing the annual prevalence of antibiotic resistance per country in Europe from 2012 – 2016, and the quarterly prevalence of antibiotic resistance per clinical commissioning group in England from 2015 – 2018. We combined these with data on rates of possible covariates of resistance. These data were used to compare the previously published forecasting models, with other commonly used forecasting models, including one geospatial model. Covariates were incorporated into the geospatial model to assess their relationship with antibiotic resistance. Results: For the European data, which was recorded on a coarse spatiotemporal scale, a naïve forecasting model was consistently the most accurate of any of the forecasting models tested. The geospatial model did not improve on this accuracy. However, it did provide some evidence that antibiotic consumption can partially explain the distribution of resistance. The English data were aggregated at a finer scale, and expected-trend-seasonal (ETS) forecasts were the most accurate. The geospatial model did not significantly improve upon the median accuracy of the ETS model, but it appeared to be less sensitive to noise in the data, and provided evidence that rates of antibiotic prescription and bacteraemia are correlated with resistance. Conclusion: Annual, national-level surveillance data appears to be insufficient for fitting accurate antibiotic resistance forecasting models, but there is evidence that data collected at a finer spatiotemporal scale could be used to improve forecast accuracy. Additionally, incorporating antibiotic prescription or consumption data into the model could improve the predictive accuracy.

Cross-feeding modulates the rate and mechanism of antibiotic resistance evolution in a model microbial community of Escherichia coli and Salmonella enterica

With antibiotic resistance rates on the rise, it is critical to understand how microbial species interactions influence the evolution of resistance. In obligate mutualisms, the survival of any one species (regardless of its intrinsic resistance) is contingent on the resistance of its cross-feeding partners. This sets the community antibiotic sensitivity at that of the 'weakest link' species. In this study, we tested the hypothesis that weakest link dynamics in an obligate cross-feeding relationship would limit the extent and mechanisms of antibiotic resistance evolution. We experimentally evolved an obligate co-culture and monoculture controls along gradients of two different antibiotics. We measured the rate at which each treatment increased antibiotic resistance, and sequenced terminal populations to question whether mutations differed between mono- and co-cultures. In both rifampicin and ampicillin treatments, we observed that resistance evolved more slowly in obligate co-cultures of E. coli and S. enterica than in monocultures. While we observed similar mechanisms of resistance arising under rifampicin selection, under ampicillin selection different resistance mechanisms arose in co-cultures and monocultures. In particular, mutations in an essential cell division protein, ftsI, arose in S. enterica only in co-culture. A simple mathematical model demonstrated that reliance on a partner is sufficient to slow the rate of adaptation, and can change the distribution of adaptive mutations that are acquired. Our results demonstrate that cooperative metabolic interactions can be an important modulator of resistance evolution in microbial communities.

Population structure across scales facilitates coexistence and spatial heterogeneity of antibiotic-resistant infections

Antibiotic-resistant infections are a growing threat to human health, but basic features of the eco-evolutionary dynamics remain unexplained. Most prominently, there is no clear mechanism for the long-term coexistence of both drug-sensitive and resistant strains at intermediate levels, a ubiquitous pattern seen in surveillance data. Here we show that accounting for structured or spatially-heterogeneous host populations and variability in antibiotic consumption can lead to persistent coexistence over a wide range of treatment coverages, drug efficacies, costs of resistance, and mixing patterns. Moreover, this mechanism can explain other puzzling spatiotemporal features of drug-resistance epidemiology that have received less attention, such as large differences in the prevalence of resistance between geographical regions with similar antibiotic consumption or that neighbor one another. We find that the same amount of antibiotic use can lead to very different levels of resistance depending on how treatment is distributed in a transmission network. We also identify parameter regimes in which population structure alone cannot support coexistence, suggesting the need for other mechanisms to explain the epidemiology of antibiotic resistance. Our analysis identifies key features of host population structure that can be used to assess resistance risk and highlights the need to include spatial or demographic heterogeneity in models to guide resistance management.

VERA: agent-based modeling transmission of antibiotic resistance between human pathogens and gut microbiota

MOTIVATION

The resistance of bacterial pathogens to antibiotics is one of the most important issues of modern health care. The human microbiota can accumulate resistance determinants and transfer them to pathogenic microbiota by means of horizontal gene transfer. Thus, it is important to develop methods of prediction and monitoring of antibiotics resistance in human populations.

RESULTS

We present the agent-based VERA model, which allows simulation of the spread of pathogens, including the possible horizontal transfer of resistance determinants from a commensal microbiota community. The model considers the opportunity of residents to stay in the town or in a medical institution, have incorrect self-treatment, treatment with several antibiotics types and transfer and accumulation of resistance determinants from commensal microorganism to a pathogen. In this model, we have also created an assessment of optimum observation frequency of infection spread among the population. Investigating model behavior, we show a number of non-linear dependencies, including the exponential nature of the dependence of the total number of those infected on the average resistance of a pathogen. As the model infection, we chose infection with Shigella spp., though it could be applied to a wide range of other pathogens.

AVAILABILITY AND IMPLEMENTATION

Source code and binaries VERA and VERA.viewer are freely available for download at github.com/lpenguin/microbiota-resistome. The code is written in Java, JavaScript and R for Linux platform.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Modeling Antibiotic Use Strategies in Intensive Care Units: Comparing De-escalation and Continuation

Antimicrobial de-escalation refers to the treatment mechanism of switching from empiric antibiotics with good coverage to alternatives based on laboratory susceptibility test results, with the aim of avoiding unnecessary use of broad-spectrum antibiotics. In a previous study, we have developed multi-strain and multi-drug models in an intensive care unit setting, to evaluate the benefits and trade-offs of de-escalation in comparison with the conventional strategy called antimicrobial continuation. Our simulation results indicated that for a large portion of credible parameter combinations, de-escalation reduces the use of the empiric antibiotic but increases the probabilities of colonization and infections. In this paper, we first simplify the previous models to compare the long-term dynamical behaviors between de-escalation and continuation systems under a two-strain scenario. The analytical results coincide with our previous findings in the complex models, indicating the benefits and unintended consequences of de-escalation strategy result from the nature of this treatment mechanism, not from the complexity of the high-dimensional systems. By extending the models to three-strain scenarios, we find that de-escalation is superior than continuation in preventing outbreaks of invading strains that are resistant to empiric antibiotics. Thus decisions on antibiotic use strategies should be made specifically according to ICU conditions and intervention objectives.

On the probability of strain invasion in endemic settings: Accounting for individual heterogeneity and control in multi-strain dynamics

•

Endemic infection can insulate host populations from invasion by mutant variants.

•

The timing of control implementation strongly influences its efficacy.

•

Controls that exacerbate host heterogeneity outperform those that curtail it.

•

Differential control can facilitate strain invasion and eventual replacement.

Pathogen evolution is an imminent threat to global health that has warranted, and duly received, considerable attention within the medical, microbiological and modelling communities. Outbreaks of new pathogens are often ignited by the emergence and transmission of mutant variants descended from wild-type strains circulating in the community. In this work we investigate the stochastic dynamics of the emergence of a novel disease strain, introduced into a population in which it must compete with an existing endemic strain. In analogy with past work on single-strain epidemic outbreaks, we apply a branching process approximation to calculate the probability that the new strain becomes established. As expected, a critical determinant of the survival prospects of any invading strain is the magnitude of its reproduction number relative to that of the background endemic strain. Whilst in most circumstances this ratio must exceed unity in order for invasion to be viable, we show that differential control scenarios can lead to less-fit novel strains invading populations hosting a fitter endemic one. This analysis and the accompanying findings will inform our understanding of the mechanisms that have led to past instances of successful strain invasion, and provide valuable lessons for thwarting future drug-resistant strain incursions.

Predicting effects of changed antimicrobial usage on the abundance of antimicrobial resistance genes in finisher' gut microbiomes

It is accepted that usage of antimicrobials (AMs) in food animals causes the emergence and spread of antimicrobial resistance (AMR) in this sector, while also contributing to the burden of AMR in humans. Curbing the increasing occurrence of AMR in food animals requires in-depth knowledge of the quantitative relationship between antimicrobial usage (AMU) and AMR to achieve desired resistance reductions from interventions targeting AMU. In the observational study, the relationships between lifetime AMU in 83 finisher batches from Danish farms and the AMR gene abundances of seven antimicrobial classes in their gut microbiomes were quantified using multi-variable linear regression models. These relationships and the national lifetime AMU in pigs were included in the predictive modelling that allowed for testing of scenarios with changed lifetime AMU for finishers produced in Denmark in 2014. A total of 50 farms from the observational study were included in validating the observational study and the predictive modelling. The results from the observational study showed that the relationship was linear, and that the parenteral usage of AMs had a high effect on specific AM-classes of resistance, whereas the peroral usage had a lower but broader effect on several classes. Three different scenarios of changed lifetime AMU were simulated in the predictive modelling. When all tetracycline usage ceased, the predicted interval reductions of aminoglycoside, lincosamide and tetracycline resistance were 4-42 %, 0-8 % and 9-18 %, respectively. When the peroral tetracycline usage of the 10 % highest users was replaced with peroral macrolide usage, the tetracycline resistance fell by 1-2 % and the macrolide and MLSb resistance increased by 5-8 %. When all extended-spectrum penicillin usage was replaced with parenteral lincosamide usage, the beta-lactam resistance fell by 2-7 %, but the lincosamide usage and resistance increased by 194 % and 10-45 %, respectively. The external validation provided results within the 95 % CI of the predictive modelling outcome at national level, while the external validation at farm level was less accurate. In conclusion, interventions targeting AMU will reduce AMR abundance, though differently depending on the targeted AM-class and provided the reduction of one AM-class usage is not replaced with usage of another AM-class. Predicting several classes of AMR gene abundance simultaneously will support stakeholders when deciding on interventions targeting AMU in the finisher production to avoid adverse and unforeseen effects on the AMR abundance. This study provides a sound predictive modelling framework for further development, including the dynamics of AMU on AMR in finishers at national level.

The effect of spatiotemporal antibiotic inhomogeneities on the evolution of resistance

Combating the evolution of widespread antibiotic resistance is one of the most pressing challenges facing modern medicine. Recent research has demonstrated that the evolution of pathogens with high levels of resistance can be accelerated by spatial and temporal inhomogeneities in antibiotic concentration, which frequently arise in patients and the environment. Strategies to predict and counteract the effects of such inhomogeneities will be critical in the fight against resistance. In this paper we develop a mechanistic framework for modelling the adaptive evolution of resistance in the presence of spatiotemporal antibiotic concentrations, which treats the adaptive process as an interaction between two mutually orthogonal forces; the first returns cells to their wild-type state in the absence of antibiotic selection, and the second selects for increased coping ability in the presence of an antibiotic. We apply our model to investigate laboratory adaptation experiments, and then extend it to consider the case in which multiple strategies for resistance undergo competitive evolution.

Quantifying uncertainty about future antimicrobial resistance: Comparing structured expert judgment and statistical forecasting methods

The increase of multidrug resistance and resistance to last-line antibiotics is a major global public health threat. Although surveillance programs provide useful current and historical information on the scale of the problem, the future emergence and spread of antibiotic resistance is uncertain, and quantifying this uncertainty is crucial for guiding decisions about investment in antibiotics and resistance control strategies. Mathematical and statistical models capable of projecting future rates are challenged by the paucity of data and the complexity of the emergence and spread of resistance, but experts have relevant knowledge. We use the Classical Model of structured expert judgment to elicit projections with uncertainty bounds of resistance rates through 2026 for nine pathogen-antibiotic pairs in four European countries and empirically validate the assessments against data on a set of calibration questions. The performance-weighted combination of experts in France, Spain, and the United Kingdom projected that resistance for five pairs on the World Health Organization’s priority pathogens list (E. coli and K. pneumoniae resistant to third-generation cephalosporins and carbapenems and MRSA) would remain below 50% in 2026. In Italy, although upper bounds of 90% credible ranges exceed 50% resistance for some pairs, the medians suggest Italy will sustain or improve its current rates. We compare these expert projections to statistical forecasts based on historical data from the European Antimicrobial Resistance Surveillance Network (EARS-Net). Results from the statistical models differ from each other and from the judgmental forecasts in many cases. The judgmental forecasts include information from the experts about the impact of current and future shifts in infection control, antibiotic usage, and other factors that cannot be easily captured in statistical forecasts, demonstrating the potential of structured expert judgment as a tool for better understanding the uncertainty about future antibiotic resistance.

The Relative Impact of Community and Hospital Antibiotic Use on the Selection of Extended-spectrum Beta-lactamase-producing Escherichia coli

Antibiotic stewardship programs have traditionally focused on reducing hospital antibiotic use. However, reducing community antibiotic prescribing could have substantial impacts in both hospital and community settings. We developed a deterministic model of transmission of extended-spectrum beta-lactamase-producing Escherichia coli in both the community and hospitals. We fit the model to existing, national-level antibiotic use and resistance prevalence data from Sweden. Across a range of conditions, a given relative change in antibiotic use in the community had a greater impact on resistance prevalence in both the community and hospitals than an equivalent relative change in hospital use. However, on a per prescription basis, changes in antibiotic use in hospitals had the greatest impact. The magnitude of changes in prevalence were modest, even with large changes in antimicrobial use. These data support the expansion of stewardship programs/interventions beyond the walls of hospitals, but also suggest that such efforts would benefit hospitals themselves.

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.

Resistance diagnostics as a public health tool to combat antibiotic resistance: A model-based evaluation

Rapid point-of-care resistance diagnostics (POC-RD) are a key tool in the fight against antibiotic resistance. By tailoring drug choice to infection genotype, doctors can improve treatment efficacy while limiting costs of inappropriate antibiotic prescription. Here, we combine epidemiological theory and data to assess the potential of resistance diagnostics (RD) innovations in a public health context, as a means to limit or even reverse selection for antibiotic resistance. POC-RD can be used to impose a nonbiological fitness cost on resistant strains by enabling diagnostic-informed treatment and targeted interventions that reduce resistant strains' opportunities for transmission. We assess this diagnostic-imposed fitness cost in the context of a spectrum of bacterial population biologies and find that POC-RD have a greater potential against obligate pathogens than opportunistic pathogens already subject to selection under "bystander" antibiotic exposure during asymptomatic carriage (e.g., the pneumococcus). We close by generalizing the notion of RD-informed strategies to incorporate carriage surveillance information and illustrate that coupling transmission-control interventions to the discovery of resistant strains in carriage can potentially select against resistance in a broad range of opportunistic pathogens.

Dynamics of Drug Resistance: Optimal Control of an Infectious Disease

Antimicrobial resistance is a significant public health threat. In the U.S. alone, 2 million people are infected and 23,000 die each year from antibiotic resistant bacterial infections. In many cases, infections are resistant to all but a few remaining drugs. We examine the case where a single drug remains and solve for the optimal treatment policy for an SIS infectious disease model incorporating the effects of drug resistance. The problem is formulated as an optimal control problem with two continuous state variables, the disease prevalence and drug's "quality" (the fraction of infections that are drug-susceptible). The decision maker's objective is to minimize the discounted cost of the disease to society over an infinite horizon. We provide a new generalizable solution approach that allows us to thoroughly characterize the optimal treatment policy analytically. We prove that the optimal treatment policy is a bang-bang policy with a single switching time. The action/inaction regions can be described by a single boundary that is strictly increasing when viewed as a function of drug quality, indicating that when the disease transmission rate is constant, the policy of withholding treatment to preserve the drug for a potentially more serious future outbreak is not optimal. We show that the optimal value function and/or its derivatives are neither C ¹ nor Lipschitz continuous suggesting that numerical approaches to this family of dynamic infectious disease models may not be computationally stable. Furthermore, we demonstrate that relaxing the standard assumption of constant disease transmission rate can fundamentally change the shape of the action region, add a singular arc to the optimal control, and make preserving the drug for a serious outbreak optimal. In addition, we apply our framework to the case of antibiotic resistant gonorrhea.

Evolutionary epidemiology models to predict the dynamics of antibiotic resistance

The evolution of resistance to antibiotics is a major public health problem and an example of rapid adaptation under natural selection by antibiotics. The dynamics of antibiotic resistance within and between hosts can be understood in the light of mathematical models that describe the epidemiology and evolution of the bacterial population. "Between-host" models describe the spread of resistance in the host community, and in more specific settings such as hospitalized hosts (treated by antibiotics at a high rate), or farm animals. These models make predictions on the best strategies to limit the spread of resistance, such as reducing transmission or adapting the prescription of several antibiotics. Models can be fitted to epidemiological data in the context of intensive care units or hospitals to predict the impact of interventions on resistance. It has proven harder to explain the dynamics of resistance in the community at large, in particular because models often do not reproduce the observed coexistence of drug-sensitive and drug-resistant strains. "Within-host" models describe the evolution of resistance within the treated host. They show that the risk of resistance emergence is maximal at an intermediate antibiotic dose, and some models successfully explain experimental data. New models that include the complex host population structure, the interaction between resistance-determining loci and other loci, or integrating the within- and between-host levels will allow better interpretation of epidemiological and genomic data from common pathogens and better prediction of the evolution of resistance.

Simulating Multilevel Dynamics of Antimicrobial Resistance in a Membrane Computing Model

Membrane computing is a bio-inspired computing paradigm whose devices are the so-called membrane systems or P systems. The P system designed in this work reproduces complex biological landscapes in the computer world. It uses nested "membrane-surrounded entities" able to divide, propagate, and die; to be transferred into other membranes; to exchange informative material according to flexible rules; and to mutate and be selected by external agents. This allows the exploration of hierarchical interactive dynamics resulting from the probabilistic interaction of genes (phenotypes), clones, species, hosts, environments, and antibiotic challenges. Our model facilitates analysis of several aspects of the rules that govern the multilevel evolutionary biology of antibiotic resistance. We examined a number of selected landscapes where we predict the effects of different rates of patient flow from hospital to the community and vice versa, the cross-transmission rates between patients with bacterial propagules of different sizes, the proportion of patients treated with antibiotics, and the antibiotics and dosing found in the opening spaces in the microbiota where resistant phenotypes multiply. We also evaluated the selective strengths of some drugs and the influence of the time 0 resistance composition of the species and bacterial clones in the evolution of resistance phenotypes. In summary, we provide case studies analyzing the hierarchical dynamics of antibiotic resistance using a novel computing model with reciprocity within and between levels of biological organization, a type of approach that may be expanded in the multilevel analysis of complex microbial landscapes.IMPORTANCE The work that we present here represents the culmination of many years of investigation in looking for a suitable methodology to simulate the multihierarchical processes involved in antibiotic resistance. Everything started with our early appreciation of the different independent but embedded biological units that shape the biology, ecology, and evolution of antibiotic-resistant microorganisms. Genes, plasmids carrying these genes, cells hosting plasmids, populations of cells, microbial communities, and host's populations constitute a complex system where changes in one component might influence the other ones. How would it be possible to simulate such a complexity of antibiotic resistance as it occurs in the real world? Can the process be predicted, at least at the local level? A few years ago, and because of their structural resemblance to biological systems, we realized that membrane computing procedures could provide a suitable frame to approach these questions. Our manuscript describes the first application of this modeling methodology to the field of antibiotic resistance and offers a bunch of examples-just a limited number of them in comparison with the possible ones to illustrate its unprecedented explanatory power.

Modeling the Growth and Decline of Pathogen Effective Population Size Provides Insight into Epidemic Dynamics and Drivers of Antimicrobial Resistance

Nonparametric population genetic modeling provides a simple and flexible approach for studying demographic history and epidemic dynamics using pathogen sequence data. Existing Bayesian approaches are premised on stochastic processes with stationary increments which may provide an unrealistic prior for epidemic histories which feature extended period of exponential growth or decline. We show that nonparametric models defined in terms of the growth rate of the effective population size can provide a more realistic prior for epidemic history. We propose a nonparametric autoregressive model on the growth rate as a prior for effective population size, which corresponds to the dynamics expected under many epidemic situations. We demonstrate the use of this model within a Bayesian phylodynamic inference framework. Our method correctly reconstructs trends of epidemic growth and decline from pathogen genealogies even when genealogical data are sparse and conventional skyline estimators erroneously predict stable population size. We also propose a regression approach for relating growth rates of pathogen effective population size and time-varying variables that may impact the replicative fitness of a pathogen. The model is applied to real data from rabies virus and Staphylococcus aureus epidemics. We find a close correspondence between the estimated growth rates of a lineage of methicillin-resistant S. aureus and population-level prescription rates of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} }{}$\beta$\end{document}-lactam antibiotics. The new models are implemented in an open source R package called skygrowth which is available at https://github.com/mrc-ide/skygrowth.

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.

Application of dynamic modelling techniques to the problem of antibacterial use and resistance: a scoping review

Selective pressure exerted by the widespread use of antibacterial drugs is accelerating the development of resistant bacterial populations. The purpose of this scoping review was to summarise the range of studies that use dynamic models to analyse the problem of bacterial resistance in relation to antibacterial use in human and animal populations. A comprehensive search of the peer-reviewed literature was performed and non-duplicate articles (n = 1486) were screened in several stages. Charting questions were used to extract information from the articles included in the final subset (n = 81). Most studies (86%) represent the system of interest with an aggregate model; individual-based models are constructed in only seven articles. There are few examples of inter-host models outside of human healthcare (41%) and community settings (38%). Resistance is modelled for a non-specific bacterial organism and/or antibiotic in 40% and 74% of the included articles, respectively. Interventions with implications for antibacterial use were investigated in 67 articles and included changes to total antibiotic consumption, strategies for drug management and shifts in category/class use. The quality of documentation related to model assumptions and uncertainty varies considerably across this subset of articles. There is substantial room to improve the transparency of reporting in the antibacterial resistance modelling literature as is recommended by best practice guidelines.

In silico analysis of antibiotic-induced Clostridium difficile infection: Remediation techniques and biological adaptations

In this paper we study antibiotic-induced C. difficile infection (CDI), caused by the toxin-producing C. difficile (CD), and implement clinically-inspired simulated treatments in a computational framework that synthesizes a generalized Lotka-Volterra (gLV) model with SIR modeling techniques. The gLV model uses parameters derived from an experimental mouse model, in which the mice are administered antibiotics and subsequently dosed with CD. We numerically identify which of the experimentally measured initial conditions are vulnerable to CD colonization, then formalize the notion of CD susceptibility analytically. We simulate fecal transplantation, a clinically successful treatment for CDI, and discover that both the transplant timing and transplant donor are relevant to the the efficacy of the treatment, a result which has clinical implications. We incorporate two nongeneric yet dangerous attributes of CD into the gLV model, sporulation and antibiotic-resistant mutation, and for each identify relevant SIR techniques that describe the desired attribute. Finally, we rely on the results of our framework to analyze an experimental study of fecal transplants in mice, and are able to explain observed experimental results, validate our simulated results, and suggest model-motivated experiments.

An evolutionary model to predict the frequency of antibiotic resistance under seasonal antibiotic use, and an application to Streptococcus pneumoniae

The frequency of resistance to antibiotics in Streptococcus pneumoniae has been stable over recent decades. For example, penicillin non-susceptibility in Europe has fluctuated between 12% and 16% without any major time trend. In spite of long-term stability, resistance fluctuates over short time scales, presumably in part due to seasonal fluctuations in antibiotic prescriptions. Here, we develop a model that describes the evolution of antibiotic resistance under selection by multiple antibiotics prescribed at seasonally changing rates. This model was inspired by, and fitted to, published data on monthly antibiotics prescriptions and frequency of resistance in two communities in Israel over 5 years. Seasonal fluctuations in antibiotic usage translate into small fluctuations of the frequency of resistance around the average value. We describe these dynamics using a perturbation approach that encapsulates all ecological and evolutionary forces into a generic model, whose parameters quantify a force stabilizing the frequency of resistance around the equilibrium and the sensitivity of the population to antibiotic selection. Fitting the model to the data revealed a strong stabilizing force, typically two to five times stronger than direct selection due to antibiotics. The strong stabilizing force explains that resistance fluctuates in phase with usage, as antibiotic selection alone would result in resistance fluctuating behind usage with a lag of three months when antibiotic use is seasonal. While most antibiotics selected for increased resistance, intriguingly, cephalosporins selected for decreased resistance to penicillins and macrolides, an effect consistent in the two communities. One extra monthly prescription of cephalosporins per 1000 children decreased the frequency of penicillin-resistant strains by 1.7%. This model emerges under minimal assumptions, quantifies the forces acting on resistance and explains up to 43% of the temporal variation in resistance.

Why sensitive bacteria are resistant to hospital infection control

Background: Large reductions in the incidence of antibiotic-resistant strains of Staphylococcus aureus and Clostridium difficile have been observed in response to multifaceted hospital-based interventions. Reductions in antibiotic-sensitive strains have been smaller or non-existent. It has been argued that since infection control measures, such as hand hygiene, should affect resistant and sensitive strains equally, observed changes must have largely resulted from other factors, including changes in antibiotic use. We used a mathematical model to test the validity of this reasoning. Methods: We developed a mechanistic model of resistant and sensitive strains in a hospital and its catchment area. We assumed the resistant strain had a competitive advantage in the hospital and the sensitive strain an advantage in the community. We simulated a hospital hand hygiene intervention that directly affected resistant and sensitive strains equally. The annual incidence rate ratio ( IRR) associated with the intervention was calculated for hospital- and community-acquired infections of both strains. Results: For the resistant strain, there were large reductions in hospital-acquired infections (0.1 ≤ IRR ≤ 0.6) and smaller reductions in community-acquired infections (0.2 ≤ IRR ≤  0.9). These reductions increased in line with increasing importance of nosocomial transmission of the strain. For the sensitive strain, reductions in hospital acquisitions were much smaller (0.6 ≤ IRR ≤ 0.9), while communityacquisitions could increase or decrease (0.9 ≤ IRR ≤ 1.2). The greater the importance of the community environment for the transmission of the sensitive strain, the smaller the reductions. Conclusions: Counter-intuitively, infection control interventions, including hand hygiene, can have strikingly discordant effects on resistant and sensitive strains even though they target them equally, following differences in their adaptation to hospital and community-based transmission. Observed lack of effectiveness of control measures for sensitive strains does not provide evidence that infection control interventions have been ineffective in reducing resistant strains.

Why sensitive bacteria are resistant to hospital infection control

Background: Large reductions in the incidence of antibiotic-resistant strains of Staphylococcus aureus and Clostridium difficile have been observed in response to multifaceted hospital-based interventions. Reductions in antibiotic-sensitive strains have been smaller or non-existent. It has been argued that since infection control measures, such as hand hygiene, should affect resistant and sensitive strains equally, observed changes must have largely resulted from other factors, including changes in antibiotic use. We used a mathematical model to test the validity of this reasoning.

Methods: We developed a mechanistic model of resistant and sensitive strains in a hospital and its catchment area. We assumed the resistant strain had a competitive advantage in the hospital and the sensitive strain an advantage in the community. We simulated a hospital hand hygiene intervention that directly affected resistant and sensitive strains equally. The annual incidence rate ratio ( IRR) associated with the intervention was calculated for hospital- and community-acquired infections of both strains.

Results: For the resistant strain, there were large reductions in hospital-acquired infections (0.1 ≤ IRR ≤ 0.6) and smaller reductions in community-acquired infections (0.2 ≤ IRR ≤  0.9). These reductions increased in line with increasing importance of nosocomial transmission of the strain. For the sensitive strain, reductions in hospital acquisitions were much smaller (0.6 ≤ IRR ≤ 0.9), while communityacquisitions could increase or decrease (0.9 ≤ IRR ≤ 1.2). The greater the importance of the community environment for the transmission of the sensitive strain, the smaller the reductions.

Conclusions: Counter-intuitively, infection control interventions, including hand hygiene, can have strikingly discordant effects on resistant and sensitive strains even though they target them equally, following differences in their adaptation to hospital and community-based transmission. Observed lack of effectiveness of control measures for sensitive strains does not provide evidence that infection control interventions have been ineffective in reducing resistant strains.

How to Use a Chemotherapeutic Agent When Resistance to It Threatens the Patient

When resistance to anticancer or antimicrobial drugs evolves in a patient, highly effective chemotherapy can fail, threatening patient health and lifespan. Standard practice is to treat aggressively, effectively eliminating drug-sensitive target cells as quickly as possible. This prevents sensitive cells from acquiring resistance de novo but also eliminates populations that can competitively suppress resistant populations. Here we analyse that evolutionary trade-off and consider recent suggestions that treatment regimens aimed at containing rather than eliminating tumours or infections might more effectively delay the emergence of resistance. Our general mathematical analysis shows that there are situations in which regimens aimed at containment will outperform standard practice even if there is no fitness cost of resistance, and, in those cases, the time to treatment failure can be more than doubled. But, there are also situations in which containment will make a bad prognosis worse. Our analysis identifies thresholds that define these situations and thus can guide treatment decisions. The analysis also suggests a variety of interventions that could be used in conjunction with cytotoxic drugs to inhibit the emergence of resistance. Fundamental principles determine, across a wide range of disease settings, the circumstances under which standard practice best delays resistance emergence-and when it can be bettered.

Benefits and unintended consequences of antimicrobial de-escalation: Implications for stewardship programs

Sequential antimicrobial de-escalation aims to minimize resistance to high-value broad-spectrum empiric antimicrobials by switching to alternative drugs when testing confirms susceptibility. Though widely practiced, the effects de-escalation are not well understood. Definitions of interventions and outcomes differ among studies. We use mathematical models of the transmission and evolution of Pseudomonas aeruginosa in an intensive care unit to assess the effect of de-escalation on a broad range of outcomes, and clarify expectations. In these models, de-escalation reduces the use of high-value drugs and preserves the effectiveness of empiric therapy, while also selecting for multidrug-resistant strains and leaving patients vulnerable to colonization and superinfection. The net effect of de-escalation in our models is to increase infection prevalence while also increasing the probability of effective treatment. Changes in mortality are small, and can be either positive or negative. The clinical significance of small changes in outcomes such as infection prevalence and death may exceed more easily detectable changes in drug use and resistance. Integrating harms and benefits into ranked outcomes for each patient may provide a way forward in the analysis of these tradeoffs. Our models provide a conceptual framework for the collection and interpretation of evidence needed to inform antimicrobial stewardship.

Proteomic profile of susceptible and multidrug-resistant clinical isolates of Escherichia coli and Klebsiella pneumoniae using label-free and immunoproteomic strategies

Infectious diseases caused by multidrug-resistant (MDR) Enterobacteriaceae have exponentially increased in the past decade, and are a major concern in hospitals. In the first part of the work, we compared the proteome profile of MDR and susceptible clinical isolates of Escherichia coli and Klebsiella pneumoniae in order to identify possible biological processes associated with drug resistance and susceptible phenotypes, using a label-free approach. In the second part, we used an immunoproteomics approach to identify immunoreactive proteins in the same isolates. A total of 388 and 377 proteins were identified in MDR and susceptible E. coli, respectively, evidencing that biological processes related to translation are upregulated in E. coli MDR, while there is an upregulation of processes related to catalytic activity in K. pneumoniae MDR. Both MDR strains show downregulation of processes related to amino acid activation and tRNA amino-acylation. Our data also suggest that MDR strains have higher immunoreactivity than the susceptible strains. The application of high-throughput mass spectrometry (MS) and bioinformatics to the study of modulation of biological processes might shed light on the characterization of multidrug resistance in bacteria.

How to measure the impacts of antibiotic resistance and antibiotic development on empiric therapy: new composite indices

OBJECTIVES

We aimed to construct widely useable summary measures of the net impact of antibiotic resistance on empiric therapy. Summary measures are needed to communicate the importance of resistance, plan and evaluate interventions, and direct policy and investment.

DESIGN, SETTING AND PARTICIPANTS

As an example, we retrospectively summarised the 2011 cumulative antibiogram from a Toronto academic intensive care unit.

OUTCOME MEASURES

We developed two complementary indices to summarise the clinical impact of antibiotic resistance and drug availability on empiric therapy. The Empiric Coverage Index (ECI) measures susceptibility of common bacterial infections to available empiric antibiotics as a percentage. The Empiric Options Index (EOI) varies from 0 to 'the number of treatment options available', and measures the empiric value of the current stock of antibiotics as a depletable resource. The indices account for drug availability and the relative clinical importance of pathogens. We demonstrate meaning and use by examining the potential impact of new drugs and threatening bacterial strains.

CONCLUSIONS

In our intensive care unit coverage of device-associated infections measured by the ECI remains high (98%), but 37-44% of treatment potential measured by the EOI has been lost. Without reserved drugs, the ECI is 86-88%. New cephalosporin/β-lactamase inhibitor combinations could increase the EOI, but no single drug can compensate for losses. Increasing methicillin-resistant Staphylococcus aureus (MRSA) prevalence would have little overall impact (ECI=98%, EOI=4.8-5.2) because many Gram-positives are already resistant to β-lactams. Aminoglycoside resistance, however, could have substantial clinical impact because they are among the few drugs that provide coverage of Gram-negative infections (ECI=97%, EOI=3.8-4.5). Our proposed indices summarise the local impact of antibiotic resistance on empiric coverage (ECI) and available empiric treatment options (EOI) using readily available data. Policymakers and drug developers can use the indices to help evaluate and prioritise initiatives in the effort against antimicrobial resistance.

Harnessing Intra-Host Strain Competition to Limit Antibiotic Resistance: Mathematical Model Results

Antibiotic overuse has promoted the spread of antibiotic resistance. To compound the issue, treating individuals dually infected with antibiotic-resistant and antibiotic-vulnerable strains can make their infections completely resistant through competitive release. We formulate mathematical models of transmission dynamics accounting for dual infections and extensions accounting for lag times between infection and treatment or between cure and ending treatment. Analysis using the Next-Generation Matrix reveals how competition within hosts and the costs of resistance determine whether vulnerable and resistant strains persist, coexist, or drive each other to extinction. Invasion analysis predicts that treatment of dually infected cases will promote resistance. By varying antibiotic strength, the models suggest that physicians have two ways to achieve a particular resistance target: prescribe relatively weak antibiotics to everyone infected with an antibiotic-vulnerable strain or give more potent prescriptions to only those patients singly infected with the vulnerable strain after ruling out the possibility of them being dually infected with resistance. Through selectivity and moderation in antibiotic prescription, resistance might be limited.