The population genetics of antibiotic resistance. II: Analytic theory for sustained populations of bacteria in a community of hosts

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.

A unified inter-host and in-host model of antibiotic resistance and infection spread in a hospital ward

As the battle continues against hospital-acquired infections and the concurrent rise in antibiotic resistance among many of the major causative pathogens, there is a dire need to conduct controlled experiments, in order to compare proposed control strategies. However, cost, time, and ethical considerations make this evaluation strategy either impractical or impossible to implement with living patients. This paper presents a multi-scale model that offers promise as the basis for a tool to simulate these (and other) controlled experiments. This is a "unified" model in two important ways: (i) It combines inter-host and in-host dynamics into a single model, and (ii) it links two very different modeling approaches - agent-based modeling and differential equations - into a single model. The potential of this model as an instrument to combat antibiotic resistance in hospitals is demonstrated with numerical examples.

Mathematical modelling of antimicrobial resistance in agricultural waste highlights importance of gene transfer rate

Antimicrobial resistance is of global concern. Most antimicrobial use is in agriculture; manures and slurry are especially important because they contain a mix of bacteria, including potential pathogens, antimicrobial resistance genes and antimicrobials. In many countries, manures and slurry are stored, especially over winter, before spreading onto fields as organic fertilizer. Thus, these are a potential location for gene exchange and selection for resistance. We develop and analyse a mathematical model to quantify the spread of antimicrobial resistance in stored agricultural waste. We use parameters from a slurry tank on a UK dairy farm as an exemplar. We show that the spread of resistance depends in a subtle way on the rates of gene transfer and antibiotic inflow. If the gene transfer rate is high, then its reduction controls resistance, while cutting antibiotic inflow has little impact. If the gene transfer rate is low, then reducing antibiotic inflow controls resistance. Reducing length of storage can also control spread of resistance. Bacterial growth rate, fitness costs of carrying antimicrobial resistance and proportion of resistant bacteria in animal faeces have little impact on spread of resistance. Therefore, effective treatment strategies depend critically on knowledge of gene transfer rates.

Contribution of mathematical modeling to the fight against bacterial antibiotic resistance

PURPOSE OF REVIEW

Modeling of antibiotic resistance in pathogenic bacteria responsible for human disease has developed considerably over the last decade. Herein, we summarize the main published studies to illustrate the contribution of models for understanding both within-host and population-based phenomena. We then suggest possible topics for future studies.

RECENT FINDINGS

Model building of bacterial resistance has involved epidemiologists, biologists and modelers with two different objectives. First, modeling has helped largely in identifying and understanding the factors and biological phenomena responsible for the emergence and spread of resistant strains. Second, these models have become important decision support tools for medicine and public health.

SUMMARY

Major improvements of models in the coming years should take into account specific pathogen characteristics (resistance mechanisms, multiple colonization phenomena, cooperation and competition among species) and better description of the contacts associated with transmission risk within populations.

What is the mechanism for persistent coexistence of drug-susceptible and drug-resistant strains of Streptococcus pneumoniae?

The rise of antimicrobial resistance in many pathogens presents a major challenge to the treatment and control of infectious diseases. Furthermore, the observation that drug-resistant strains have risen to substantial prevalence but have not replaced drug-susceptible strains despite continuing (and even growing) selective pressure by antimicrobial use presents an important problem for those who study the dynamics of infectious diseases. While simple competition models predict the exclusion of one strain in favour of whichever is 'fitter', or has a higher reproduction number, we argue that in the case of Streptococcus pneumoniae there has been persistent coexistence of drug-sensitive and drug-resistant strains, with neither approaching 100 per cent prevalence. We have previously proposed that models seeking to understand the origins of coexistence should not incorporate implicit mechanisms that build in stable coexistence 'for free'. Here, we construct a series of such 'structurally neutral' models that incorporate various features of bacterial spread and host heterogeneity that have been proposed as mechanisms that may promote coexistence. We ask to what extent coexistence is a typical outcome in each. We find that while coexistence is possible in each of the models we consider, it is relatively rare, with two exceptions: (i) allowing simultaneous dual transmission of sensitive and resistant strains lets coexistence become a typical outcome, as does (ii) modelling each strain as competing more strongly with itself than with the other strain, i.e. self-immunity greater than cross-immunity. We conclude that while treatment and contact heterogeneity can promote coexistence to some extent, the in-host interactions between strains, particularly the interplay between coinfection, multiple infection and immunity, play a crucial role in the long-term population dynamics of pathogens with drug resistance.

Models of fungicide resistance dynamics

We describe two classes of models used for fungicide and antibiotic resistance dynamics. One class assumes that the density of the pathogen (or severity of the disease caused by the pathogen) has no feedback effects on the rate at which new infections arise. The second class does not make this assumption. A quantitative relationship between these two classes is derived. We then discuss the two sets of assumptions made in the literature about initial conditions: either both the fungicide-sensitive strain and the -resistant strain are initially at low density, or the sensitive strain is resident at nonlow density and the resistant strain is initially at low density. We show that models of fungicide resistance dynamics with and without density-dependent feedback give contrasting predictions on the effects of pathogen life-cycle parameters and the effects of the fungicide (dose, frequency, use of mixtures, spatial usage restrictions) on the evolution, invasion, and spread of fungicide resistance. We further show that the evaluation of a resistance management strategy requires a very precise definition of what constitutes a good strategy.

Structure of the scientific community modelling the evolution of resistance

Faced with the recurrent evolution of resistance to pesticides and drugs, the scientific community has developed theoretical models aimed at identifying the main factors of this evolution and predicting the efficiency of resistance management strategies. The evolutionary forces considered by these models are generally similar for viruses, bacteria, fungi, plants or arthropods facing drugs or pesticides, so interaction between scientists working on different biological organisms would be expected. We tested this by analysing co-authorship and co-citation networks using a database of 187 articles published from 1977 to 2006 concerning models of resistance evolution to all major classes of pesticides and drugs. These analyses identified two main groups. One group, led by ecologists or agronomists, is interested in agricultural crop or stock pests and diseases. It mainly uses a population genetics approach to model the evolution of resistance to insecticidal proteins, insecticides, herbicides, antihelminthic drugs and miticides. By contrast, the other group, led by medical scientists, is interested in human parasites and mostly uses epidemiological models to study the evolution of resistance to antibiotic and antiviral drugs. Our analyses suggested that there is also a small scientific group focusing on resistance to antimalaria drugs, and which is only poorly connected with the two larger groups. The analysis of cited references indicates that each of the two large communities publishes its research in a different set of literature and has its own keystone references: citations with a large impact in one group are almost never cited by the other. We fear the lack of exchange between the two communities might slow progress concerning resistance evolution which is currently a major issue for society.

The rising impact of mathematical modelling in epidemiology: antibiotic resistance research as a case study

Mathematical modelling of infectious diseases has gradually become part of public health decision-making in recent years. However, the developing status of modelling in epidemiology and its relationship with other relevant scientific approaches have never been assessed quantitatively. Herein, using antibiotic resistance as a case study, 60 published models were analysed. Their interactions with other scientific fields are reported and their citation impact evaluated, as well as temporal trends. The yearly number of antibiotic resistance modelling publications increased significantly between 1990 and 2006. This rise cannot be explained by the surge of interest in resistance phenomena alone. Moreover, modelling articles are, on average, among the most frequently cited third of articles from the journal in which they were published. The results of this analysis, which might be applicable to other emerging public health problems, demonstrate the growing interest in mathematical modelling approaches to evaluate antibiotic resistance.

What is the role of quality circles in strategies to optimise antibiotic prescribing? A pragmatic cluster-randomised controlled trial in primary care

OBJECTIVE

To evaluate the effect on antibiotic prescribing of an intervention in existing local quality circles promoting an evidence-based guideline for acute rhinosinusitis.

DESIGN

A pragmatic cluster-randomised controlled trial comparing standard dissemination of the guideline by mail with an additional strategy using quality circles.

SETTING

General practice in Flanders, Belgium.

PARTICIPANTS

General practitioners (GPs) in 18 local quality circles were randomly allocated to two study arms. All GPs received the guideline by mail. GPs in the nine quality circles allocated to the intervention arm received an additional group intervention, which consisted of one self-led meeting using material introduced to the group moderator by a member of the research team.

MAIN OUTCOME MEASURES

Adherence to the guideline was measured as differences in the proportion of antibiotic prescriptions, including the choice of antibiotic, between the two study arms after the intervention period. GPs registered their encounters with patients presenting with signs and symptoms of acute rhinosinusitis in a booklet designed for the study.

RESULTS

A total of 75 doctors (29% of GPs in the participating quality circles) registered 408 consultations. In the intervention group, 56.9% of patients received an antibiotic compared with 58.3% in the control group. First-choice antibiotics were issued in 34.5% of antibiotic prescriptions in the intervention group compared with 29.4% in the control group. After adjusting for patient and GP characteristics, the ORadj for antibiotics prescribed in the intervention arm compared with the control arm was 0.63 (95% CI 0.29 to 1.37). There was no effect on the choice of antibiotic (ORadj 1.07, 95% CI 0.34 to 3.37).

CONCLUSION

A single intervention in quality circles of GPs integrated in the group's normal working procedure did not have a significant effect on the quality of antibiotic prescribing. More attention to the context and structure of primary care practice, and insight into the process of self-reflective learning may provide clues to optimise the effectiveness of quality circles.

The role of compensatory mutations in the emergence of drug resistance

Pathogens that evolve resistance to drugs usually have reduced fitness. However, mutations that largely compensate for this reduction in fitness often arise. We investigate how these compensatory mutations affect population-wide resistance emergence as a function of drug treatment. Using a model of gonorrhea transmission dynamics, we obtain generally applicable, qualitative results that show how compensatory mutations lead to more likely and faster resistance emergence. We further show that resistance emergence depends on the level of drug use in a strongly nonlinear fashion. We also discuss what data need to be obtained to allow future quantitative predictions of resistance emergence.

Stakeholder position paper: epidemiological perspectives on antibiotic use in animals

Epidemiologists studying antimicrobial resistance are often interested in analyzing the association between antimicrobial resistance and antimicrobial use in animals, and on the impact of antimicrobial use in animals on the occurrence of resistance in bacteria affecting human populations. Given the various potential antimicrobial use data sources, it seems likely there will be some variability in the utility of the data for interpreting trends in antimicrobial resistance and investigating the relationship between antimicrobial use in animals and antimicrobial resistance in bacteria affecting human health. From an epidemiologic perspective, the major issues related to incorporation of antimicrobial use data into antimicrobial resistance monitoring programs are the further development of epidemiologic methods for collecting, quantifying, analyzing and interpreting use data; an open and realistic consideration of the limitations of the data; developing an understanding of scaling, temporal and spatial heterogeneity issues; and the interpretative problems of ecologic and atomistic fallacy. Given the many potential biases in antimicrobial use data, attempts to relate levels of antimicrobial use to levels of antimicrobial resistance should be done with caution until the data are better understood and the aforementioned issues have been addressed.

Interventions to improve antibiotic prescribing practices in ambulatory care

BACKGROUND

The development of resistance to antibiotics by many important human pathogens has been linked to exposure to antibiotics over time. The misuse of antibiotics for viral infections (for which they are of no value) and the excessive use of broad spectrum antibiotics in place of narrower spectrum antibiotics have been well-documented throughout the world. Many studies have helped to elucidate the reasons physicians use antibiotics inappropriately.

OBJECTIVES

To systematically review the literature to estimate the effectiveness of professional interventions, alone or in combination, in improving the selection, dose and treatment duration of antibiotics prescribed by healthcare providers in the outpatient setting; and to evaluate the impact of these interventions on reducing the incidence of antimicrobial resistant pathogens.

SEARCH STRATEGY

We searched the Cochrane Effective Practice and Organisation of Care Group (EPOC) specialized register for studies relating to antibiotic prescribing and ambulatory care. Additional studies were obtained from the bibliographies of retrieved articles, the Scientific Citation Index and personal files.

SELECTION CRITERIA

We included all randomised and quasi-randomised controlled trials (RCT and QRCT), controlled before and after studies (CBA) and interrupted time series (ITS) studies of healthcare consumers or healthcare professionals who provide primary care in the outpatient setting. Interventions included any professional intervention, as defined by EPOC, or a patient-based intervention.

DATA COLLECTION AND ANALYSIS

Two review authors independently extracted data and assessed study quality.

MAIN RESULTS

Thirty-nine studies examined the effect of printed educational materials for physicians, audit and feedback, educational meetings, educational outreach visits, financial and healthcare system changes, physician reminders, patient-based interventions and multi-faceted interventions. These interventions addressed the overuse of antibiotics for viral infections, the choice of antibiotic for bacterial infections such as streptococcal pharyngitis and urinary tract infection, and the duration of use of antibiotics for conditions such as acute otitis media. Use of printed educational materials or audit and feedback alone resulted in no or only small changes in prescribing. The exception was a study documenting a sustained reduction in macrolide use in Finland following the publication of a warning against their use for group A streptococcal infections. Interactive educational meetings appeared to be more effective than didactic lectures. Educational outreach visits and physician reminders produced mixed results. Patient-based interventions, particularly the use of delayed prescriptions for infections for which antibiotics were not immediately indicated effectively reduced antibiotic use by patients and did not result in excess morbidity. Multi-faceted interventions combining physician, patient and public education in a variety of venues and formats were the most successful in reducing antibiotic prescribing for inappropriate indications. Only one of four studies demonstrated a sustained reduction in the incidence of antibiotic-resistant bacteria associated with the intervention.

AUTHORS' CONCLUSIONS

The effectiveness of an intervention on antibiotic prescribing depends to a large degree on the particular prescribing behaviour and the barriers to change in the particular community. No single intervention can be recommended for all behaviours in any setting. Multi-faceted interventions where educational interventions occur on many levels may be successfully applied to communities after addressing local barriers to change. These were the only interventions with effect sizes of sufficient magnitude to potentially reduce the incidence of antibiotic-resistant bacteria. Future research should focus on which elements of these interventions are the most effective. In addition, patient-based interventions and physician reminders show promise and innovative methods such as these deserve further study.

Purifying selection and demographic expansion affect sequence diversity of the ligand-binding domain of a glutamate-gated chloride channel gene of Haemonchus placei

Ninety-five genomic sequences of the ligand-binding domain of glutamate-gated chloride channel genes of three populations of the parasitic nematode H. placei were evaluated for patterns of diversity, demography, and selection. These genes code for subunits of ion channels, which are involved in the mode of action of the most commonly used antiparasitic drugs, the macrocyclic lactones. An extremely high frequency of unique segregating sites in exons and introns was observed, with significantly negative neutrality tests in each population for noncoding, synonymous, and nonsynonymous sites. Several tests indicated that support for balancing selection, positive selection, and hitchhiking was lacking. McDonald-Kreitman tests using H. contortus or C. elegans as an outgroup revealed an extreme excess of replacement polymorphism, consistent with weak purifying selection. Although these tests agree that negative selection may explain the excess of replacement changes, an alternative interpretation is required for the significantly negative Fu and Li's D statistics based on silent and noncoding sites. These include homogeneous forces such as background selection and demographic expansion. The lack of population subdivision and the negative values of Tajima's D for this outbreeding parasitic nematode render background selection less likely than demographic expansion. Comparison of D statistics based on different site types using neutral coalescent simulations supported this interpretation. Although this statistic was more negative for nonsynonymous sites than for synonymous sites, most comparisons of the D statistic were not significantly different between mutation classes. A few significant site comparisons were also consistent with demographic expansion, because the observed test statistic ( D(neutral) - D(selected)) were low relative to the neutral expectations. Finally, previous mitochondrial studies also identified a demographic expansion of this parasitic nematode species, which lends further support to a scenario involving both demographic and purifying forces in the ligand-binding domain of H. placei.

Arming the enemy: the evolution of resistance to self-proteins

A remarkable range of novel antibiotics is attracting increasing interest as a major new weapon in the campaign against bacterial infection. They are based on the toxic peptides that provide the innate immune system of animals, and it is claimed that bacteria will be unable to evolve resistance to them because they attack the 'Achilles' heel' of bacterial membrane structure. Both experimental evidence and theoretical arguments suggest that this claim is doubtful. If so, the introduction of these substances into general use may provoke the evolution of resistance to our own defence proteins and thus compromise our natural defences against infection.

Changes in antibiotic-prescribing practices and carriage of penicillin-resistant Streptococcus pneumoniae: A controlled intervention trial in rural Alaska

From 1998 to 2000, 13 rural Alaskan villages (population, 3326) were surveyed annually by nasopharyngeal cultures for Streptococcus pneumoniae carriage. Data regarding antibiotic use for the entire population was abstracted from clinic records. In 1999, education of medical providers and the community about appropriate antibiotic use began in 4 villages; this program was expanded to include all villages in 2000. Antibiotic courses per person decreased by 31% in the initial intervention villages and by 35% in the remaining villages after education (P<.01 for each). Samples were obtained for culture from a mean of 31% of the population each year; 31% carried pneumococcus. No sustained decrease in carriage of penicillin-nonsusceptible strains was observed. When linear regression was used, serotype accounted for 81% of the variance in pneumococcal minimum inhibitory concentrations after the intervention, compared with 7% for antibiotic use. This suggests that reducing the carriage of serotypes associated with antibiotic resistance by use of pneumococcal conjugate vaccines may have a greater short-term impact than does decreasing antibiotic use.

Minimizing potential resistance: a population dynamics view

I examine the results of studies that used mathematical models of the epidemiology and population genetics of antibiotic treatment and resistance in open communities and in hospitals to explore the following issues: the relationship between antibiotic consumption and the frequency of antibiotic resistance in bacterial populations in communities and in hospitals; methods of controlling the growth, dissemination, and persistence of antibiotic resistance in these settings; the extent to which resistance can be controlled; and the speed with which the effects of control measures will be realized. In open communities, it will take years or even decades to see substantial reductions in the frequency of antibiotic resistance solely as a result of more prudent (reduced) use of antibiotics. However, if we can restrict the input of resistant bacteria into hospitals, through the application of infection control and other measures, it should be possible to reduce the frequency of resistance and even eliminate resistant bacteria from these institutions in short order.

Antibiotic and insecticide resistance modeling--is it time to start talking?

Mathematical models have played an important part in understanding both antibiotic and insecticide resistance. However, there has been little, if any, interdisciplinary work between these two areas of active research. One primary reason for this is that bacterial population genetics differ substantially from the population genetics of diploid organisms. This article examines these differences and their effect on resistance. It explores what efforts have gone into modeling resistance mathematically in both arenas, and offers suggestions on how the two groups could work together to gain a more comprehensive understanding of the resistance phenomenon

Additive effects of a two-amino-acid insertion and a single-amino-acid substitution in dihydropteroate synthase for the development of sulphonamide-resistant Neisseria meningitidis

Sulphonamide resistance in some clinical isolates of Neisseria meningitidis is associated with an insertion in the chromosomal folP gene leading to the addition of two amino acids, serine and glycine, in the drug target enzyme dihydropteroate synthase (DHPS). Removal of the insertion resulted in a markedly higher Km for the substrate p-aminobenzoic acid and a markedly lower Km for 2-amino-4-hydroxy-6-(hydroxymethyl)-7,8-dihydropteridine pyrophosphate. In the same isolates an additional important difference, compared to wild-type enzymes, was found at amino acid position 68, which is a proline in most DHPS enzymes, but is serine in one and leucine in another clinical isolate of sulphonamide-resistant N. meningitidis. The alteration at position 68 was found to affect mainly the level of sulphonamide resistance and had only a minor effect on the Km for the substrates. Introduction of the serine-glycine dipeptide at position 194 and a proline to serine substitution at position 68 in DHPS from normal, susceptible N. meningitidis failed to produce a functional sulphonamide-resistant enzyme. The conclusion of this study is that it is not possible to change a normal chromosomally encoded DHPS of N. meningitidis to a sulphonamide-resistant one simply by an insertion of serine and glycine as seen in clinical isolates. It is likely that the resistance gene found in clinical isolates has evolved in another bacterial species where a combination of other amino acid changes may have contributed to produce a functionally resistant enzyme. This new resistance gene may have then been introduced into N. meningitidis by natural transformation.

Compensatory mutations, antibiotic resistance and the population genetics of adaptive evolution in bacteria

In the absence of the selecting drugs, chromosomal mutations for resistance to antibiotics and other chemotheraputic agents commonly engender a cost in the fitness of microorganisms. Recent in vivo and in vitro experimental studies of the adaptation to these "costs of resistance" in Escherichia coli, HIV, and Salmonella typhimurium found that evolution in the absence of these drugs commonly results in the ascent of mutations that ameliorate these costs, rather than higher-fitness, drug-sensitive revertants. To ascertain the conditions under which this compensatory evolution, rather than reversion, will occur, we did computer simulations, in vitro experiments, and DNA sequencing studies with low-fitness rpsL (streptomycin-resistant) mutants of E. coli with and without mutations that compensate for the fitness costs of these ribosomal protein mutations. The results of our investigation support the hypothesis that in these experiments, the ascent of intermediate-fitness compensatory mutants, rather than high-fitness revertants, can be attributed to higher rates of compensatory mutations relative to that of reversion and to the numerical bottlenecks associated with serial passage. We argue that these bottlenecks are intrinsic to the population dynamics of parasitic and commensal microbes and discuss the implications of these results to the problem of drug resistance and adaptive evolution in parasitic and commmensal microorganisms in general.

The epidemiology of antibiotic resistance in hospitals: paradoxes and prescriptions

A simple mathematical model of bacterial transmission within a hospital was used to study the effects of measures to control nosocomial transmission of bacteria and reduce antimicrobial resistance in nosocomial pathogens. The model predicts that: (i) Use of an antibiotic for which resistance is not yet present in a hospital will be positively associated at the individual level (odds ratio) with carriage of bacteria resistant to other antibiotics, but negatively associated at the population level (prevalence). Thus inferences from individual risk factors can yield misleading conclusions about the effect of antibiotic use on resistance to another antibiotic. (ii) Nonspecific interventions that reduce transmission of all bacteria within a hospital will disproportionately reduce the prevalence of colonization with resistant bacteria. (iii) Changes in the prevalence of resistance after a successful intervention will occur on a time scale of weeks to months, considerably faster than in community-acquired infections. Moreover, resistance can decline rapidly in a hospital even if it does not carry a fitness cost. The predictions of the model are compared with those of other models and published data. The implications for resistance control and study design are discussed, along with the limitations and assumptions of the model.

Alterations in the conjunctival bacterial flora following a single dose of azithromycin in a trachoma endemic area

BACKGROUND/AIMS

The World Health Organisation has recommended repeated mass treatment of children in trachoma endemic areas with oral azithromycin. While chlamydia, the causative agent of trachoma, remains universally sensitive to azithromycin, there is concern that large scale programmes may alter the bacterial flora and induce resistance in streptococcal species. In this study the effect of a single dose of azithromcyin on the prevalence, species distribution, and resistance of conjunctival bacterial flora was determined.

METHODS

Baseline and 14 day follow up bacterial cultures were taken from the conjunctivae of 121 children who reside in a trachoma endemic area of Nepal. 91 children were treated with azithromycin at baseline and 31 children received deferred treatment at the 14 day follow up.

RESULTS

Although the prevalence of bacterial pathogens decreased significantly with azithromycin treatment, a significant change in the distribution of specific bacterial pathogens could not be demonstrated. Streptococcal resistance to azithromycin was found significantly more frequently after treatment. No change in the prevalence, distribution, or resistance pattern was found in the untreated control group.

CONCLUSION

Repeated mass treatment of trachoma endemic areas with oral azithromycin will have an effect on bacterial flora. However, further work needs to be done to determine if this will have any clinical relevance.

Antibiotic use in humans and bacterial resistance

As with any public health problem, the evolution of antibacterial resistance must be viewed from a perspective of risk, and analysed in terms of probabilities within the populations. It is necessary to be able to predict the risk of antibacterial resistance, in the future, and two main strategies have recently been developed in mathematical models that may help to evaluate these risks. It is also important to understand how antibiotics are used and how their use affects the evolution of antibacterial resistance. Understanding the epidemiology of antibacterial resistance will enable us to develop preventive strategies to limit existing resistance and to avoid the emergence of new strains of resistant bacteria.