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

Precision epidemiology at the nexus of mathematics and nanotechnology: Unraveling the dance of viral dynamics

The intersection of mathematical modeling, nanotechnology, and epidemiology marks a paradigm shift in our battle against infectious diseases, aligning with the focus of the journal on the regulation, expression, function, and evolution of genes in diverse biological contexts. This exploration navigates the intricate dance of viral transmission dynamics, highlighting mathematical models as dual tools of insight and precision instruments, a theme relevant to the diverse sections of Gene. In the context of virology, ethical considerations loom large, necessitating robust frameworks to protect individual rights, an aspect essential in infectious disease research. Global collaboration emerges as a critical pillar in our response to emerging infectious diseases, fortified by the predictive prowess of mathematical models enriched by nanotechnology. The synergy of interdisciplinary collaboration, training the next generation to bridge mathematical rigor, biology, and epidemiology, promises accelerated discoveries and robust models that account for real-world complexities, fostering innovation and exploration in the field. In this intricate review, mathematical modeling in viral transmission dynamics and epidemiology serves as a guiding beacon, illuminating the path toward precision interventions, global preparedness, and the collective endeavor to safeguard human health, resonating with the aim of advancing knowledge in gene regulation and expression.

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.

Putting sheep scab in its place: A more relational approach

Since the reintroduction of sheep scab within the UK, its prevalence has increased despite several industry-led initiatives to control and manage the disease. Some studies have suggested that initiatives or policies should instead focus on specific places, such as geographically high-risk areas for sheep scab, which could allow for a more targeted approach. However, this risk of sheep scab has been measured in set geographical areas, without the reference to the interplay of topography, host, pathogen and the way in which humans socially and culturally define risk and place, potentially limiting the effectiveness of preventative initiatives. Therefore, the aim of the current study was to understand how place influences sheep farmers' approaches to the identification and management of the risk of sheep scab in their flocks. Qualitative data was collected from 43 semi-structured interviews with sheep farmers from England, Scotland, and Wales and was analysed by using the constant comparative approach. The codes were grouped into four concepts that influenced farmers' decision-making strategies for sheep scab control: perception of place; risk identification; risk categorisation; and risk management. These concepts were used as an analytical framework to identify three different 'places': 'uncontrollable places', 'liminal places' and 'protective places'. Each place reflects a different sheep scab control strategy used by farmers and shaped by their perceptions of place and risk. The 'uncontrollable places' category represented farmers who were located in areas that were geographically high-risk for sheep scab and who experienced a high frequency of sheep scab infestations in their flocks. The risk posed by their local landscape and neighbouring farmers, who neglected to engage in preventative behaviours, led them to feel unable to engage in effective risk management. Thus, they viewed scab as uncontrollable. The farmers within the 'liminal places' category were characterised as farmers who were located in high-risk areas for sheep scab, but experienced low levels of sheep scab infestations. These farmers characterised the risks associated with sheep scab management in terms of needing to protect their reputation and felt more responsibility for controlling sheep scab, which influenced them to engage in more protective measures. The farmers within the 'protective places' category were characterised as farming within low-risk areas and thus experienced a low level of sheep scab infestations. These farmers also described their risk in terms of their reputation and the responsibility they held for protecting others. However, they sought to rely on their low geographical risk of sheep scab as a main source of protection and therefore did not always engage in protective measures. These results suggest that place-based effects have significant impacts on sheep farmers' beliefs and behaviours and thus should be considered by policymakers when developing future strategies for sheep scab control.

Mathematical Modeling Research Output Impacting New Technological Development: An Axiomatization to Build Novelty

The mathematical modeling of research-based output impacting new technology development is crucial for a developing country. However, the complexity of modern mathematical modeling research output makes it unclear over how it can impact the development of new technology. Therefore, this study aims to explore, categorize and formulize the axioms of mathematical modeling research output that impacts the development of new technology. Seven participants were involved in this research. Interviews were conducted to explore their remarkable mathematical modeling output and how the output can impact the development of new technology. The categorization axioms are: i. mathematical modeling for theorizing, ii. mathematical modeling for simulations, iii. mathematical modeling for useable innovation and iv. patent and product commercialization. Finally, the categorization can be formulized as an axiom of mathematical modeling novelty, which is the desired research output. Moreover, patents and commercialization are the elements that mathematical modeling should possess for new technological development. The limited number of participants involved in this study makes this study formulation limited to only some types of mathematical modeling output. However, this substantive formulation could give some ideas in proposing the path and processes on how to enhance the effort for society to develop the culture of mathematical modeling in developing new technology.

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.

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

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

Integer Versus Fractional Order SEIR Deterministic and Stochastic Models of Measles

In this paper, we compare the performance between systems of ordinary and (Caputo) fractional differential equations depicting the susceptible-exposed-infectious-recovered (SEIR) models of diseases. In order to understand the origins of both approaches as mean-field approximations of integer and fractional stochastic processes, we introduce the fractional differential equations (FDEs) as approximations of some type of fractional nonlinear birth and death processes. Then, we examine validity of the two approaches against empirical courses of epidemics; we fit both of them to case counts of three measles epidemics that occurred during the pre-vaccination era in three different locations. While ordinary differential equations (ODEs) are commonly used to model epidemics, FDEs are more flexible in fitting empirical data and theoretically offer improved model predictions. The question arises whether, in practice, the benefits of using FDEs over ODEs outweigh the added computational complexities. While important differences in transient dynamics were observed, the FDE only outperformed the ODE in one of out three data sets. In general, FDE modeling approaches may be worth it in situations with large refined data sets and good numerical algorithms.

Population-level mathematical modeling of antimicrobial resistance: a systematic review

BACKGROUND

Mathematical transmission models are increasingly used to guide public health interventions for infectious diseases, particularly in the context of emerging pathogens; however, the contribution of modeling to the growing issue of antimicrobial resistance (AMR) remains unclear. Here, we systematically evaluate publications on population-level transmission models of AMR over a recent period (2006-2016) to gauge the state of research and identify gaps warranting further work.

METHODS

We performed a systematic literature search of relevant databases to identify transmission studies of AMR in viral, bacterial, and parasitic disease systems. We analyzed the temporal, geographic, and subject matter trends, described the predominant medical and behavioral interventions studied, and identified central findings relating to key pathogens.

RESULTS

We identified 273 modeling studies; the majority of which (> 70%) focused on 5 infectious diseases (human immunodeficiency virus (HIV), influenza virus, Plasmodium falciparum (malaria), Mycobacterium tuberculosis (TB), and methicillin-resistant Staphylococcus aureus (MRSA)). AMR studies of influenza and nosocomial pathogens were mainly set in industrialized nations, while HIV, TB, and malaria studies were heavily skewed towards developing countries. The majority of articles focused on AMR exclusively in humans (89%), either in community (58%) or healthcare (27%) settings. Model systems were largely compartmental (76%) and deterministic (66%). Only 43% of models were calibrated against epidemiological data, and few were validated against out-of-sample datasets (14%). The interventions considered were primarily the impact of different drug regimens, hygiene and infection control measures, screening, and diagnostics, while few studies addressed de novo resistance, vaccination strategies, economic, or behavioral changes to reduce antibiotic use in humans and animals.

CONCLUSIONS

The AMR modeling literature concentrates on disease systems where resistance has been long-established, while few studies pro-actively address recent rise in resistance in new pathogens or explore upstream strategies to reduce overall antibiotic consumption. Notable gaps include research on emerging resistance in Enterobacteriaceae and Neisseria gonorrhoeae; AMR transmission at the animal-human interface, particularly in agricultural and veterinary settings; transmission between hospitals and the community; the role of environmental factors in AMR transmission; and the potential of vaccines to combat AMR.

Medical prescribing and antibiotic resistance: A game-theoretic analysis of a potentially catastrophic social dilemma

The availability of antibiotics presents medical practitioners with a prescribing dilemma. On the one hand, antibiotics provide a safe and effective treatment option for patients with bacterial infections, but at a population level, over-prescription reduces their effectiveness by facilitating the evolution of bacteria that are resistant to antibiotic medication. A game-theoretic investigation, including analysis of equilibrium strategies, evolutionarily stability, and replicator dynamics, reveals that rational doctors, motivated to attain the best outcomes for their own patients, will prescribe antibiotics irrespective of the level of antibiotic resistance in the population and the behavior of other doctors, although they would achieve better long-term outcomes if their prescribing were more restrained. Ever-increasing antibiotic resistance may therefore be inevitable unless some means are found of modifying the payoffs of this potentially catastrophic social dilemma.

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.

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.

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.

Moving interdisciplinary science forward: integrating participatory modelling with mathematical modelling of zoonotic disease in Africa

This review outlines the benefits of using multiple approaches to improve model design and facilitate multidisciplinary research into infectious diseases, as well as showing and proposing practical examples of effective integration. It looks particularly at the benefits of using participatory research in conjunction with traditional modelling methods to potentially improve disease research, control and management. Integrated approaches can lead to more realistic mathematical models which in turn can assist with making policy decisions that reduce disease and benefit local people. The emergence, risk, spread and control of diseases are affected by many complex bio-physical, environmental and socio-economic factors. These include climate and environmental change, land-use variation, changes in population and people’s behaviour. The evidence base for this scoping review comes from the work of a consortium, with the aim of integrating modelling approaches traditionally used in epidemiological, ecological and development research. A total of five examples of the impacts of participatory research on the choice of model structure are presented. Example 1 focused on using participatory research as a tool to structure a model. Example 2 looks at identifying the most relevant parameters of the system. Example 3 concentrates on identifying the most relevant regime of the system (e.g., temporal stability or otherwise), Example 4 examines the feedbacks from mathematical models to guide participatory research and Example 5 goes beyond the so-far described two-way interplay between participatory and mathematical approaches to look at the integration of multiple methods and frameworks. This scoping review describes examples of best practice in the use of participatory methods, illustrating their potential to overcome disciplinary hurdles and promote multidisciplinary collaboration, with the aim of making models and their predictions more useful for decision-making and policy formulation.

Population Dynamics of Patients with Bacterial Resistance in Hospital Environment

During the past decades, the increase of antibiotic resistance has become a major concern worldwide. The researchers found that superbugs with new type of resistance genes (NDM-1) have two aspects of transmission characteristics; the first is that the antibiotic resistance genes can horizontally transfer among bacteria, and the other is that the superbugs can spread between humans through direct contact. Based on these two transmission mechanisms, we study the dynamics of population in hospital environment where superbugs exist. In this paper, we build three mathematic models to illustrate the dynamics of patients with bacterial resistance in hospital environment. The models are analyzed using stability theory of differential equations. Positive equilibrium points of the system are investigated and their stability analysis is carried out. Moreover, the numerical simulation of the proposed model is also performed which supports the theoretical findings.

Understanding the mechanisms and drivers of antimicrobial resistance

To combat the threat to human health and biosecurity from antimicrobial resistance, an understanding of its mechanisms and drivers is needed. Emergence of antimicrobial resistance in microorganisms is a natural phenomenon, yet antimicrobial resistance selection has been driven by antimicrobial exposure in health care, agriculture, and the environment. Onward transmission is affected by standards of infection control, sanitation, access to clean water, access to assured quality antimicrobials and diagnostics, travel, and migration. Strategies to reduce antimicrobial resistance by removing antimicrobial selective pressure alone rely upon resistance imparting a fitness cost, an effect not always apparent. Minimising resistance should therefore be considered comprehensively, by resistance mechanism, microorganism, antimicrobial drug, host, and context; parallel to new drug discovery, broad ranging, multidisciplinary research is needed across these five levels, interlinked across the health-care, agriculture, and environment sectors. Intelligent, integrated approaches, mindful of potential unintended results, are needed to ensure sustained, worldwide access to effective antimicrobials.

How fitness reduced, antimicrobial resistant bacteria survive and spread: a multiple pig-multiple bacterial strain model

More than 30% of E. coli strains sampled from pig farms in Denmark over the last five years were resistant to the commonly used antimicrobial tetracycline. This raises a number of questions: How is this high level sustained if resistant bacteria have reduced growth rates? Given that there are multiple susceptible and resistant bacterial strains in the pig intestines, how can we describe their coexistence? To what extent does the composition of these multiple strains in individual pigs influence the total bacterial population of the pig pen? What happens to a complex population when antimicrobials are used? To investigate these questions, we created a model where multiple strains of bacteria coexist in the intestines of pigs sharing a pen, and explored the parameter limits of a stable system; both with and without an antimicrobial treatment. The approach taken is a deterministic bacterial population model with stochastic elements of bacterial distributions and transmission. The rates that govern the model are process-oriented to represent growth, excretion, and uptake from environment, independent of herd and meta-population structures. Furthermore, an entry barrier and elimination process for the individual strains in each pig were implemented. We demonstrate how competitive growth between multiple bacterial strains in individual pigs, and the transmission between pigs in a pen allow for strains of antimicrobial resistant bacteria to persist in a pig population to different extents, and how quickly they can become dominant if antimicrobial treatment is initiated. The level of spread depends in a non-linear way of the parameters that govern excretion and uptake. Furthermore, the sampling of initial distributions of strains and stochastic transmission events give rise to large variation in how homogenous and how resistant the bacterial population becomes. Most important: resistant bacteria are demonstrated to survive with a disadvantage in growth rate of well over 10%.

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.

Identifiability and estimation of multiple transmission pathways in cholera and waterborne disease

Cholera and many waterborne diseases exhibit multiple characteristic timescales or pathways of infection, which can be modeled as direct and indirect transmission. A major public health issue for waterborne diseases involves understanding the modes of transmission in order to improve control and prevention strategies. An important epidemiological question is: given data for an outbreak, can we determine the role and relative importance of direct vs. environmental/waterborne routes of transmission? We examine whether parameters for a differential equation model of waterborne disease transmission dynamics can be identified, both in the ideal setting of noise-free data (structural identifiability) and in the more realistic setting in the presence of noise (practical identifiability). We used a differential algebra approach together with several numerical approaches, with a particular emphasis on identifiability of the transmission rates. To examine these issues in a practical public health context, we apply the model to a recent cholera outbreak in Angola (2006). Our results show that the model parameters-including both water and person-to-person transmission routes-are globally structurally identifiable, although they become unidentifiable when the environmental transmission timescale is fast. Even for water dynamics within the identifiable range, when noisy data are considered, only a combination of the water transmission parameters can practically be estimated. This makes the waterborne transmission parameters difficult to estimate, leading to inaccurate estimates of important epidemiological parameters such as the basic reproduction number (R0). However, measurements of pathogen persistence time in environmental water sources or measurements of pathogen concentration in the water can improve model identifiability and allow for more accurate estimation of waterborne transmission pathway parameters as well as R0. Parameter estimates for the Angola outbreak suggest that both transmission pathways are needed to explain the observed cholera dynamics. These results highlight the importance of incorporating environmental data when examining waterborne disease.

Molecular evolution and emergence of avian gammacoronaviruses

Coronaviruses, which are single stranded, positive sense RNA viruses, are responsible for a wide variety of existing and emerging diseases in humans and other animals. The gammacoronaviruses primarily infect avian hosts. Within this genus of coronaviruses, the avian coronavirus infectious bronchitis virus (IBV) causes a highly infectious upper-respiratory tract disease in commercial poultry. IBV shows rapid evolution in chickens, frequently producing new antigenic types, which adds to the multiple serotypes of the virus that do not cross protect. Rapid evolution in IBV is facilitated by strong selection, large population sizes and high genetic diversity within hosts, and transmission bottlenecks between hosts. Genetic diversity within a host arises primarily by mutation, which includes substitutions, insertions and deletions. Mutations are caused both by the high error rate, and limited proof reading capability, of the viral RNA-dependent RNA-polymerase, and by recombination. Recombination also generates new haplotype diversity by recombining existing variants. Rapid evolution of avian coronavirus IBV makes this virus extremely difficult to diagnose and control, but also makes it an excellent model system to study viral genetic diversity and the mechanisms behind the emergence of coronaviruses in their natural host.

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.

Agent-based modeling of the spread of influenza-like illness in an emergency department: a simulation study

The objective of this paper was to develop an agent-based modeling framework in order to simulate the spread of influenza virus infection on a layout based on a representative hospital emergency department in Winnipeg, Canada. In doing so, the study complements mathematical modeling techniques for disease spread, as well as modeling applications focused on the spread of antibiotic-resistant nosocomial infections in hospitals. Twenty different emergency department scenarios were simulated, with further simulation of four infection control strategies. The agent-based modeling approach represents systems modeling, in which the emergency department was modeled as a collection of agents (patients and healthcare workers) and their individual characteristics, behaviors, and interactions. The framework was coded in C++ using Qt4 libraries running under the Linux operating system. A simple ordinary least squares (OLS) regression was used to analyze the data, in which the percentage of patients that became infected in one day within the simulation was the dependent variable. The results suggest that within the given instance context, patient-oriented infection control policies (alternate treatment streams, masking symptomatic patients) tend to have a larger effect than policies that target healthcare workers. The agent-based modeling framework is a flexible tool that can be made to reflect any given environment; it is also a decision support tool for practitioners and policymakers to assess the relative impact of infection control strategies. The framework illuminates scenarios worthy of further investigation, as well as counterintuitive findings.

Qualitative analysis of models with different treatment protocols to prevent antibiotic resistance

This paper is concerned with the qualitative analysis of two models [S. Bonhoeffer, M. Lipsitch, B.R. Levin, Evaluating treatment protocols to prevent antibiotic resistance, Proc. Natl. Acad. Sci. USA 94 (1997) 12106] for different treatment protocols to prevent antibiotic resistance. Detailed qualitative analysis about the local or global stability of the equilibria of both models is carried out in term of the basic reproduction number R(0). For the model with a single antibiotic therapy, we show that if R(0)<1, then the disease-free equilibrium is globally asymptotically stable; if R(0)>1, then the disease-endemic equilibrium is globally asymptotically stable. For the model with multiple antibiotic therapies, stabilities of various equilibria are analyzed and combining treatment is shown better than cycling treatment. Numerical simulations are performed to show that the dynamical properties depend intimately upon the parameters.

Mathematical modeling and the epidemiological research process

The authors of this paper advocate for the expanded use of mathematical models in epidemiology and provide an overview of the principles of mathematical modeling. Mathematical models can be used throughout the epidemiological research process. Initially they may help to refine study questions by visually expressing complex systems, directing literature searches, and identifying sensitive variables. In the study design phase, models can be used to test sampling strategies, to estimate sample size and power, and to predict outcomes for studies impractical due to time or ethical considerations. Once data are collected, models can assist in the interpretation of results, the exploration of causal pathways, and the combined analysis of data from multiple sources. Finally, models are commonly used in the process of applying research findings to public health practice by estimating population risk, predicting the effects of interventions, and contributing to the evaluation of ongoing programs. Mathematical modeling has the potential to make significant contributions to the field of epidemiology by enhancing the research process, serving as a tool for communicating findings to policymakers, and fostering interdisciplinary collaboration.

The impact of different antibiotic regimens on the emergence of antimicrobial-resistant bacteria

Backgroud

The emergence and ongoing spread of antimicrobial-resistant bacteria is a major public health threat. Infections caused by antimicrobial-resistant bacteria are associated with substantially higher rates of morbidity and mortality compared to infections caused by antimicrobial-susceptible bacteria. The emergence and spread of these bacteria is complex and requires incorporating numerous interrelated factors which clinical studies cannot adequately address.

Methods/Principal Findings

A model is created which incorporates several key factors contributing to the emergence and spread of resistant bacteria including the effects of the immune system, acquisition of resistance genes and antimicrobial exposure. The model identifies key strategies which would limit the emergence of antimicrobial-resistant bacterial strains. Specifically, the simulations show that early initiation of antimicrobial therapy and combination therapy with two antibiotics prevents the emergence of resistant bacteria, whereas shorter courses of therapy and sequential administration of antibiotics promote the emergence of resistant strains.

Conclusions/Significance

The principal findings suggest that (i) shorter lengths of antibiotic therapy and early interruption of antibiotic therapy provide an advantage for the resistant strains, (ii) combination therapy with two antibiotics prevents the emergence of resistance strains in contrast to sequential antibiotic therapy, and (iii) early initiation of antibiotics is among the most important factors preventing the emergence of resistant strains. These findings provide new insights into strategies aimed at optimizing the administration of antimicrobials for the treatment of infections and the prevention of the emergence of antimicrobial resistance.