Modeling and simulating the evolution of resistance against antibiotics

Interplay between strain fitness and transmission frequency determines prevalence of antimicrobial resistance

The steep rise of infections caused by bacteria that are resistant to antimicrobial agents threatens global health. However, the association between antimicrobial use and the prevalence of resistance is not straightforward. Therefore, it is necessary to quantify the importance of additional factors that affect this relationship. We theoretically explore how the prevalence of resistance is affected by the combination of three factors: antimicrobial use, bacterial transmission, and fitness cost of resistance. We present a model that combines within-host, between-hosts and between-populations dynamics, built upon the competitive Lotka-Volterra equations. We developed the model in a manner that allows future experimental validation of the findings with single isolates in the laboratory. Each host may carry two strains (susceptible and resistant) that represent the host’s commensal microbiome and are not the target of the antimicrobial treatment. The model simulates a population of hosts who are treated periodically with antibiotics and transmit bacteria to each other. We show that bacterial transmission results in strain co-existence. Transmission disseminates resistant bacteria in the population, increasing the levels of resistance. Counterintuitively, when the cost of resistance is low, high transmission frequencies reduce resistance prevalence. Transmission between host populations leads to more similar resistance levels, increasing the susceptibility of the population with higher antimicrobial use. Overall, our results indicate that the interplay between bacterial transmission and strain fitness affects the prevalence of resistance in a non-linear way. We then place our results within the context of ecological theory, particularly on temporal niche partitioning and metapopulation rescue, and we formulate testable experimental predictions for future research.

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.

Examining the impact of ICU population interaction structure on modeled colonization dynamics of Staphylococcus aureus

Background

Complex transmission models of healthcare-associated infections provide insight for hospital epidemiology and infection control efforts, but they are difficult to implement and come at high computational costs. Structuring more simplified models to incorporate the heterogeneity of the intensive care unit (ICU) patient-provider interactions, we explore how methicillin-resistant Staphylococcus aureus (MRSA) dynamics and acquisitions may be better represented and approximated.

Methods

Using a stochastic compartmental model of an 18-bed ICU, we compared the rates of MRSA acquisition across three ICU population interaction structures: a model with nurses and physicians as a single staff type (SST), a model with separate staff types for nurses and physicians (Nurse-MD model), and a Metapopulation model where each nurse was assigned a group of patients. The proportion of time spent with the assigned patient group (γ) within the Metapopulation model was also varied.

Results

The SST, Nurse-MD, and Metapopulation models had a mean of 40.6, 32.2 and 19.6 annual MRSA acquisitions respectively. All models were sensitive to the same parameters in the same direction, although the Metapopulation model was less sensitive. The number of acquisitions varied non-linearly by values of γ, with values below 0.40 resembling the Nurse-MD model, while values above that converged toward the Metapopulation structure.

Discussion

Inclusion of complex population interactions within a modeled hospital ICU has considerable impact on model results, with the SST model having more than double the acquisition rate of the more structured metapopulation model. While the direction of parameter sensitivity remained the same, the magnitude of these differences varied, producing different colonization rates across relatively similar populations. The non-linearity of the model’s response to differing values of a parameter gamma (γ) suggests simple model approximations are appropriate in only a narrow space of relatively dispersed nursing assignments.

Conclusion

Simplifying assumptions around how a hospital population is modeled, especially assuming random mixing, may overestimate infection rates and the impact of interventions. In many, if not most, cases more complex models that represent population mixing with higher granularity are justified.

Simultaneous estimation of parameters governing the vertical and horizontal transfer of antibiotic resistance genes

The accelerated spread of antibiotic resistance genes (ARG) in the environment occurs mainly through plasmid transfer facilitated via bacterial conjugation. To predict and efficiently counteract the problems associated with ARG transmission, it is important to estimate conjugation rates under different experimental conditions. The classical models typically used to estimate parameters for mating experiments, while pragmatic in calculating growth and plasmid transfer, often ignore processes such as the reduction in growth due to plasmid bearing costs and are non-inclusive of environmental influences like temperature effects. Here, we present a process-based numerical model taking into account the fitness cost associated with plasmid carriage and temperature dependencies in vertical and horizontal gene transfer processes. Observations from liquid culture conjugation experiments using Escherichia coli and the plasmid pB10 were used to validate our proposed model. We present a comparison between the parameters estimated using the existing and the proposed model. Uncertainties in the estimated parameters were quantified using classical and advanced Bayesian methods. For our mating experiments, we found that at temperatures between 20 and 37 °C, the plasmid bearing costs reduced the growth rates by > 35%. The temperature dependency model of conjugation showed a good fit (mean absolute percentage error < 10%) independent of the bacteria and the plasmid under study. The proposed model simultaneously estimates growth and plasmid transfer rate constants for all three strains (donor, recipient, and transconjugant). Simultaneous estimation of growth and conjugation parameters is particularly useful to estimate the spread of ARG when one of the mating partners inhibits the growth of the other, which is common in multi-species mating or when the incurred plasmid costs are situation dependent (e.g., increased plasmid cost in a mating environment) as observed in this study.

Modelling the effect of a dengue vaccine on reducing the evolution of resistance against antibiotic due to misuse in dengue cases

Background

This paper intends to check whether and how a hypothetical dengue vaccine could contribute to issue of evolution of bacteria resistance against antibiotics by reducing the number of patients that would inappropriately being treated with antibiotics.

Methods

We use a new mathematical model that combines, in a novel way, two previously published papers, one on the evolution of resistance against antibiotics and one classical Ross-Macdonald model for dengue transmission.

Results

The model is simulated numerically and reproduces a real case of evolution of resistance against antibiotics. In addition the model shows that the use of a hypothetical dengue vaccine could help to curb the evolution of resistance against an antibiotic inappropriately used in dengue patients. Both the increase in the proportion of resistant bacteria due to the misuse of antibiotics in dengue cases as a function of the fraction of treated patients and the reduction of that proportion as a function of vaccination coverage occur in a highly non-linear fashion.

Conclusion

The use of a dengue vaccine is helpful in reducing the rate of evolution of antibiotic resistance in a scenario of misuse of the antibiotics in dengue patients.

Antibiotic drug-resistance as a complex system driven by socio-economic growth and antibiotic misuse

Overwhelming antibiotic use poses a serious challenge today to the public-health policymakers worldwide. Many empirical studies pointed out this ever-increasing antibiotic consumption as primary driver of the community-acquired antibiotic drug-resistance, especially in the middle- and lower-income countries. The association is well documented across spatio-temporal gradients in many parts of the world, but there is rarely any study that emphasizes the mechanism of the association, which is important for combating drug-resistance. Formulating a mathematical model of emergence and transmission of drug-resistance, we in this paper, present how amalgamating three components: socio-economic growth, population ecology of infectious disease, and antibiotic misuse can instinctively incite proliferation of resistance in the society. We show that combined impact of economy, infections, and self-medication yield synergistic interactions through feedbacks on each other, presenting the emergence of drug-resistance as a self-reinforcing cycle in the population. Analysis of our model not only determines the threshold of antibiotic use beyond which the emergence of resistance may occur, but also characterizes how fast it develops depending on economic growth, and lack of education and awareness of the population. Our model illustrates that proper and timely government aid in population health can break the self-reinforcing process and reduce the burden of drug-resistance in the community.

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.

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.

Timing of pathogen adaptation to a multicomponent treatment

The sustainable use of multicomponent treatments such as combination therapies, combination vaccines/chemicals, and plants carrying multigenic resistance requires an understanding of how their population-wide deployment affects the speed of the pathogen adaptation. Here, we develop a stochastic model describing the emergence of a mutant pathogen and its dynamics in a heterogeneous host population split into various types by the management strategy. Based on a multi-type Markov birth and death process, the model can be used to provide a basic understanding of how the life-cycle parameters of the pathogen population, and the controllable parameters of a management strategy affect the speed at which a pathogen adapts to a multicomponent treatment. Our results reveal the importance of coupling stochastic mutation and migration processes, and illustrate how their stochasticity can alter our view of the principles of managing pathogen adaptive dynamics at the population level. In particular, we identify the growth and migration rates that allow pathogens to adapt to a multicomponent treatment even if it is deployed on only small proportions of the host. In contrast to the accepted view, our model suggests that treatment durability should not systematically be identified with mutation cost. We show also that associating a multicomponent treatment with defeated monocomponent treatments can be more durable than associating it with intermediate treatments including only some of the components. We conclude that the explicit modelling of stochastic processes underlying evolutionary dynamics could help to elucidate the principles of the sustainable use of multicomponent treatments in population-wide management strategies intended to impede the evolution of harmful populations.

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

Antibiotic-resistant infections complicate treatment and increase morbidity and mortality. Mathematical modeling has played an integral role in improving our understanding of antibiotic resistance. In these models, parameter sensitivity is often assessed, while model structure sensitivity is not. To examine the implications of this, we first reviewed the literature on antibiotic-resistance modeling published between 1993 and 2011. We then classified each article's model structure into one or more of 6 categories based on the assumptions made in those articles regarding within-host and population-level competition between antibiotic-sensitive and antibiotic-resistant strains. Each model category has different dynamic implications with respect to how antibiotic use affects resistance prevalence, and therefore each may produce different conclusions about optimal treatment protocols that minimize resistance. Thus, even if all parameter values are correctly estimated, inferences may be incorrect because of the incorrect selection of model structure. Our framework provides insight into model selection.

Modelling the transmission of healthcare associated infections: a systematic review

Background

Dynamic transmission models are increasingly being used to improve our understanding of the epidemiology of healthcare-associated infections (HCAI). However, there has been no recent comprehensive review of this emerging field. This paper summarises how mathematical models have informed the field of HCAI and how methods have developed over time.

Methods

MEDLINE, EMBASE, Scopus, CINAHL plus and Global Health databases were systematically searched for dynamic mathematical models of HCAI transmission and/or the dynamics of antimicrobial resistance in healthcare settings.

Results

In total, 96 papers met the eligibility criteria. The main research themes considered were evaluation of infection control effectiveness (64%), variability in transmission routes (7%), the impact of movement patterns between healthcare institutes (5%), the development of antimicrobial resistance (3%), and strain competitiveness or co-colonisation with different strains (3%). Methicillin-resistant Staphylococcus aureus was the most commonly modelled HCAI (34%), followed by vancomycin resistant enterococci (16%). Other common HCAIs, e.g. Clostridum difficile, were rarely investigated (3%). Very few models have been published on HCAI from low or middle-income countries.

The first HCAI model has looked at antimicrobial resistance in hospital settings using compartmental deterministic approaches. Stochastic models (which include the role of chance in the transmission process) are becoming increasingly common. Model calibration (inference of unknown parameters by fitting models to data) and sensitivity analysis are comparatively uncommon, occurring in 35% and 36% of studies respectively, but their application is increasing. Only 5% of models compared their predictions to external data.

Conclusions

Transmission models have been used to understand complex systems and to predict the impact of control policies. Methods have generally improved, with an increased use of stochastic models, and more advanced methods for formal model fitting and sensitivity analyses. Insights gained from these models could be broadened to a wider range of pathogens and settings. Improvements in the availability of data and statistical methods could enhance the predictive ability of models.

In-roads to the spread of antibiotic resistance: regional patterns of microbial transmission in northern coastal Ecuador

The evolution of antibiotic resistance (AR) increases treatment cost and probability of failure, threatening human health worldwide. The relative importance of individual antibiotic use, environmental transmission and rates of introduction of resistant bacteria in explaining community AR patterns is poorly understood. Evaluating their relative importance requires studying a region where they vary. The construction of a new road in a previously roadless area of northern coastal Ecuador provides a valuable natural experiment to study how changes in the social and natural environment affect the epidemiology of resistant Escherichia coli. We conducted seven bi-annual 15 day surveys of AR between 2003 and 2008 in 21 villages. Resistance to both ampicillin and sulphamethoxazole was the most frequently observed profile, based on antibiogram tests of seven antibiotics from 2210 samples. The prevalence of enteric bacteria with this resistance pair in the less remote communities was 80 per cent higher than in more remote communities (OR = 1.8 [1.3, 2.3]). This pattern could not be explained with data on individual antibiotic use. We used a transmission model to help explain this observed discrepancy. The model analysis suggests that both transmission and the rate of introduction of resistant bacteria into communities may contribute to the observed regional scale AR patterns, and that village-level antibiotic use rate determines which of these two factors predominate. While usually conceived as a main effect on individual risk, antibiotic use rate is revealed in this analysis as an effect modifier with regard to community-level risk of resistance.

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.

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.

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.

Mathematical modelling: a tool for hospital infection control

Health-care-associated infections caused by antibiotic-resistant pathogens have become a menace in hospitals worldwide and infection control measures have lead to vastly different outcomes in different countries. During the past 6 years, a theoretical framework based on mathematical models has emerged that provides solid and testable hypotheses and opens the road to a quantitative assessment of the main obstructions that undermine current efforts to control the spread of health-care-associated infections in hospitals and communities. We aim to explain to a broader audience of professionals in health care, infection control, and health systems administration some of these models that can improve the understanding of the hidden dynamics of health-care-associated infections. We also appraise their usefulness and limitations as an innovative research and decision tool for control purposes.

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

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.

Invasion thresholds for fungicide resistance: deterministic and stochastic analyses

Fungicide resistance is an important practical problem, but one that is poorly understood at the population level. Here we introduce a simple nonlinear model for fungicide resistance in botanical epidemics which includes the dynamics of the chemical control agent and the host population, while also allowing for demographic stochasticity in the host-parasite dynamics. This provides a mathematical framework for analysing the risk of fungicide resistance developing by including the parameters for the amount applied, longevity and application frequency of the fungicide. The model demonstrates the existence of thresholds for the invasion of the resistant strain in the parasite population which depend on two quantities: the relative fitness of the resistant strain and the effectiveness of control. This threshold marks a change from definite elimination of the resistant strain below the threshold to a finite probability of invasion which increases above the threshold. The fungicide decay rate, the amount of fungicide applied and the period between applications affect the effectiveness of control and, consequently, they influence whether or not resistance develops and the time taken to achieve a critical frequency of resistance. All three parameters are amenable to control by the grower or by coordinating the activity of a population of growers. Providing crude estimates of the effectiveness of control and relative fitness are available, the results can be used to predict the consequences of changing these parameters for the risk of invasion and the proportion of sites at which this might be expected to occur. Although motivated for fungicide resistance, the model has broader application to herbicide, antibiotic and antiviral resistance. The modelling approach and results are discussed in the context of resistance to chemical control in general.

Preliminary analysis of the transmission dynamics of nosocomial infections: stochastic and management effects

A simple mathematical model is developed for the spread of hand-borne nosocomial pathogens such as Staphylococcus aureus within a general medical-surgical ward. In contrast to previous models a stochastic approach is used. Computer simulations are used to explore the properties of the model, and the results are presented in terms of the pathogen's successful introduction rate, ward-level prevalence, and colonized patient-days, emphasizing the general effects of changes in management of patients and carers. Small changes in the transmissibility of the organism resulted in large changes in all three measures. Even small increases in the frequency of effective handwashes were enough to bring endemic organisms under control. Reducing the number of colonized patients admitted to the ward was also an effective control measure across a wide range of different situations. Increasing surveillance activities had little effect on the successful introduction rate but gave an almost linear reduction in colonized patient-days and ward-level prevalence. Shorter lengths of patient stay were accompanied by higher successful introduction rates, but had little effect on the other measures unless the mean time before detection of a colonized individual was large compared to the mean length of stay. We conclude that chance effects are likely to be amongst the most important factors in determining the course of an outbreak. Mathematical models can provide valuable insights into the non-linear interactions between a small number of processes, but for the very small populations found in hospital wards, a stochastic approach is essential.

Studies of antibiotic resistance within the patient, hospitals and the community using simple mathematical models

The emergence of antibiotic resistance in a wide variety of important pathogens of humans presents a worldwide threat to public health. This paper describes recent work on the use of mathematical models of the emergence and spread of resistance bacteria, on scales ranging from within the patient, in hospitals and within communities of people. Model development starts within the treated patient, and pharmacokinetic and pharmacodynamic principles are melded within a framework that mirrors the interaction between bacterial population growth, drug treatment and the immunological responses targeted at the pathogen. The model helps identify areas in which more precise information is needed, particularly in the context of how drugs influence pathogen birth and death rates (pharmacodynamics). The next area addressed is the spread of multiply drug-resistant bacteria in hospital settings. Models of the transmission dynamics of the pathogen provide a framework for assessing the relative merits of different forms of intervention, and provide criteria for control or eradication. The model is applied to the spread of vancomycin-resistant enterococci in an intensive care setting. This model framework is generalized to consider the spread of resistant organisms between hospitals. The model framework allows for heterogeneity in hospital size and highlights the importance of large hospitals in the maintenance of resistant organisms within a defined country. The spread of methicillin resistant Staphylococcus aureus (MRSA) in England and Wales provides a template for model construction and analysis. The final section addresses the emergence and spread of resistant organisms in communities of people and the dependence on the intensity of selection as measured by the volume or rate of drug use. Model output is fitted to data for Finland and Iceland and conclusions drawn concerning the key factors determining the rate of spread and decay once drug pressure is relaxed.

Population biology, evolution, and infectious disease: convergence and synthesis

Traditionally, the interest of population and evolutionary biologists in infectious diseases has been almost exclusively in their role as agents of natural selection in higher organisms. Recently, this interest has expanded to include the genetic structure and evolution of microparasite populations, the mechanisms of pathogenesis and the immune response, and the population biology, ecology, and evolutionary consequences of medical and public health interventions. This article describes recent work in these areas, emphasizing the ways in which quantitative, population-biological approaches have been contributing to the understanding of infectious disease and the design and evaluation of interventions for their treatment and prevention.

The relationship between the volume of antimicrobial consumption in human communities and the frequency of resistance

The threat to human health posed by antibiotic resistance is of growing concern. Many commensal and pathogenic organisms have developed resistance to well established and newer antibiotics. The major selection pressure driving changes in the frequency of antibiotic resistance is the volume of drug use. However, establishing a quantitative relationship between the frequency of resistance and volume of drug use has proved difficult. Using population genetic methods and epidemiological observations, we report an analysis of the influence of the selective pressure imposed by the volume of drug use on temporal changes in resistance. Analytical expressions are derived to delineate key relationships between resistance and drug consumption. The analyses indicate that the time scale for emergence of resistance under a constant selective pressure is typically much shorter than the decay time after cessation or decline in the volume of drug use and that significant reductions in resistance require equally significant reductions in drug consumption. These results highlight the need for early intervention once resistance is detected.

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

The phenomenon of antibiotic resistance is of practical importance and theoretical interest. As a foundation for further studies by simulation, experiment, and observation, we here develop a mathematical model for the dynamics of resistance among the bacteria resident in a population of hosts. The model incorporates the effects of natural selection within untreated hosts, colonization by bacteria from the environment, and the rapid increase of resistance in hosts who receive antibiotics. We derive explicit formulas for the distribution of resistance among hosts and for the rise or fall of resistance when the frequency of treatment is changed.

Resistance to antimicrobial chemotherapy: a prescription for research and action

The growing problem of resistance to antimicrobial chemotherapy was discussed by participants at the February 1995 workshop at Emory University on population biology, evolution, and control of infectious diseases. They discussed the nature and source of this problem and identified areas of research in which information is lacking for the development of programs to control of the emergence and spread of resistant bacteria. Particular attention was given to theoretical (mathematical modeling) and empirical studies of the within and between-host population biology (epidemiology) and the evolution of microbial resistance to chemotherapeutic agents. Suggestions were made about the kinds of models and data needed, and the procedures that could be employed to stem the ascent and dissemination of resistant bacteria. This article summarizes the observations and recommendations made at the 1995 meeting and in the correspondence between participants that followed. It concludes with an update on the theoretical and empirical research on the between- and within-host population biology and evolution of resistance to antimicrobial chemotherapy most of which has been done since that meeting.

The transmission dynamics of antibiotic-resistant bacteria: the relationship between resistance in commensal organisms and antibiotic consumption

We propose a mathematical model of the transmission dynamics of colonization by commensal bacteria within a human community subject to varying levels of antibiotic use designed to control morbidity induced by pathogenic strains of the normally commensal organisms. Colonization is assumed not to induce morbidity in the majority of cases, and antibiotic use is assumed to be related to the arrival and growth of pathogenic strains that give rise to infections including clinical symptoms of disease. In the absence of antibiotic resistance, the model shows how the pattern of antibiotic prescription and use can eliminate the non-pathogenic commensal strains from the host community if the fraction of people taking antibiotics with a defined efficacy exceeds some critical level. The model is extended to take account of the evolution of antibiotic resistance in the commensal population. We assume resistance may be either plasmid-mediated or conferred by selection of low-level pre-existing mutants, and that resistant organisms may experience reduced reproductive fitness. Invasion of the host community by drug-resistant commensals is possible if certain antibiotic prescribing patterns pertain. We calculate these conditions in terms of the transmission parameter of the organism and the level of antibiotic prescription and use. The model is employed to address the issues of how best to use antibiotics in populations harbouring resistant organisms, and when resistant bacteria will out-compete sensitive strains.

Evaluating treatment protocols to prevent antibiotic resistance

The spread of bacteria resistant to antimicrobial agents calls for population-wide treatment strategies to delay or reverse the trend toward antibiotic resistance. Here we propose new criteria for the evaluation of the population-wide effects of treatment protocols for directly transmitted bacterial infections and discuss different usage patterns for single and multiple antibiotic therapy. A mathematical model suggests that the long-term benefit of single drug treatment from introduction of the antibiotic until a high frequency of resistance precludes its use is almost independent of the pattern of antibiotic use. When more than one antibiotic is employed, sequential use of different antibiotics in the population ("cycling") is always inferior to treatment strategies where, at any given time, equal fractions of the population receive different antibiotics. However, treatment of all patients with a combination of antibiotics is in most cases the optimal treatment strategy.

A computer simulation model for the spread of nosocomial infections caused by multidrug-resistant pathogens

A Monte Carlo simulation model was developed for the spread of antibiotic-resistant bacteria in hospital units. The model allows for the representation of every patient and staff member. Staff-patient interactions, staff handwashing compliance, admission of colonized patients, and antibiotic use are included in the model. The simulation model provides colonization curves for patients and staff and offers the possibility of simulating different kinds of hospital units. Simulation of the spread of an antibiotic-resistant pathogen in an intensive care unit was performed. We studied the impact of handwashing compliance on colonization. The importance of handwashing in preventing colonization and the influence of admission of colonized patients in perpetuating an epidemic were confirmed by the model. The model offers a new approach to modeling the spread of nosocomial pathogens in hospital units. It allows one to study the impact of infection control measures and represents a valuable educational tool for staff.