Infectious Disease Epidemiology Department, Faculty of Epidemiology and Population Health, Centre of Mathematical Modelling, London School of Hygiene and Tropical Medicine, London, UK

Modelling and Economics unit, Public Health England, Colindale, London, UK

Abstract

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

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.

Background

Healthcare-associated infections (HCAI) continue to cause a major burden on society, affecting more than 4 million patients annually in Europe alone, and causing an estimated 16 million additional bed-days responsible for €7 billion in direct medical costs

A previous review of the area provided insight into the type of models used for hospital epidemiology and highlighted their capacity to increase epidemiological understanding, and inform infection control policy

Methods

We searched Medline (1950 to present), EMBASE (1947 to present), Scopus (1823 to present), CINAHL (1937 to present) and Global health (1910 to present). Results were limited to peer-reviewed publications in English. Search terms and Medical Subject Headings (MeSH) for nosocomial organisms and antibiotic resistance were combined with search and MeSH terms for healthcare settings and mathematical models as follows:

•Nosocomial infections in general (e.g.”

**OR**

•Nosocomial organisms (e.g. **OR** Antimicrobial resistance **AND** Nosocomial (e.g.

**AND**

•Mathematical modelling or economic evaluation model (e.g. **AND**

We decided not to use search terms for nosocomial infection types (e.g. surgical site infections or urinary tract infections), since our review focuses on the transmission of infections from one individual to another, which cannot generally be accurately represented without knowing the causative organism.

The complete search strategy is provided in the Additional file

**Search terms MEDLINE.**

Click here for file

Inclusion criteria

Eligible studies had to fulfil the following criteria: 1) mathematical modelling of HCAI transmission and/or the dynamics of antimicrobial resistance; 2) dynamic transmission models only (i.e. a model which tracks the number of individuals (or proportion of a population) carrying or infected with a pathogen over time, while capturing the effect of contact between individuals on transmission

Exclusion criteria

Studies were excluded if they did not involve: 1) human to human transmission; or did involve 2) within host transmission only; 3) pharmacodynamics and pharmacokinetics of drugs (e.g. the impact of antibiotic exposure, exploring antibiotic tolerance and investigating fitness), 4) animal transmission of HCAI; 5) community transmission of pathogens spread in the healthcare environment as well, where community spread was the focus of the paper (e.g. SARS epidemics); or 6) literature review without new primary studies. Moreover, no editorials or letters to editors were included, except if a new mathematical model was introduced.

Results

The database search retrieved 2461 unique papers (Figure

PRISMA flowchart

**PRISMA flowchart.**

The distribution of these 96 papers over time demonstrates that HCAI transmission models have been increasingly employed since the introduction of the first model of nosocomial pathogens’ spread **.**

Number of HCAI modelling publications over time (1993–2011)

**Number of HCAI modelling publications over time (1993–2011).** Number of studies identified on modelling of HCAI and antimicrobial resistance spread in a nosocomial setting according to year of publication.

Objectives of mathematical models of HCAIs

Pathogens modelled

Although HCAIs are often associated with antibiotic-resistant bacteria, HCAI models have involved antimicrobial susceptible pathogens as well. In this review, studies that did not specify a particular pathogen of concern, but that claimed to investigate antimicrobial resistant bacteria, were classified as antimicrobial resistant bacteria (ARB). Otherwise, the study was categorised as ‘HCAI in general’. Moreover, as the majority of patients can carry HCAI such as MRSA and

Figure

Pathogens modelled in a nosocomial setting (1993–2011)

**Pathogens modelled in a nosocomial setting (1993–2011).** Number of studies identified on nosocomial infection transmission according to pathogen type. MRSA= Methicillin resistant Staphylococcus aureus; ARB = Antimicrobial resistant bacteria; VRE = Vancomycin-resistant

Intervention effectiveness

The first model of HCAI conceptualised the spread of antibiotic resistance in bacterial populations among hospital patients

Main interventions evaluated over time (1993–2011)

**Main interventions evaluated over time (1993–2011).** Main interventions evaluated over time (1993–2011)**.** Illustration of the proportionate distribution of the seven most commonly investigated interventions by means of a modelling framework by the total number of publications in each time period.

**Term**

**Definition**

**Deterministic model**

A model in which there is no role of chance in the evolution of the states of the system, i.e. the model is ‘predetermined’ by the parameters and initial conditions

**Stochastic model**

A model in which random (stochastic) processes can affect whether certain events or processes occur (e.g. the rate at which individuals are infected can vary by chance)

**Compartmental model**

A model in which the population is divided into subgroups (i.e. compartments), which represent the average values of individuals in a particular state (e.g. susceptible, infectious or recovered). Within each compartment, all individuals are homogenous

**Individual-based model**

A model in which single individuals are tracked rather than subgroups. Hence, each individual can be assigned different characteristics such as the probability of acquiring infection or causing transmission

**Model fitting/ model calibration**

The inference of unknown parameters by choosing their values in order to approximate a set of data as well as possible. Examples of model fitting methods are least squares approximation maximum likelihood estimation and Markov Chain Monte Carlo Methods

**Model validation**

Comparison of model predictions to external data, that is a model should be validated against observations from alternative data to the data used for model fitting

**Univariate sensitivity analysis**

Investigation of uncertainty in model parameters and its impact on model predictions by means of altering one parameter at a time whilst holding others at their base-case value.

**Bi/ multivariate sensitivity analysis**

Investigation of uncertainty in model parameters by means of alteration of two (or more) parameters at a time whilst holding others at their base-case value.

**Probabilistic sensitivity analysis**

A type of multivariate sensitivity analysis where multiple runs of the model are performed with random selection of input parameters.

**Dynamic transmission model**

A model which tracks the number of individuals (or proportion of a population) carrying or infected with a pathogen over time, where the risk of transmission to susceptible at a given point in time is dependent on the number of infected (or colonised) individuals in the community

**Static model**

A model where the transmission risk is treated as a parameter exogenous to the model, i.e. it does not change with the number of infectious individuals in the population

**Force of infection**

The rate at which infected individuals become infected per unit time

Furthering epidemiological understanding

Models are often used to increase epidemiological understanding. Hospital surveillance data, which is frequently used to inform HCAI models, can lack detail in what is needed for modelling purposes. For example, information on asymptomatic carriage and timing of events (e.g. infection) are often lacking. Several studies use new statistical methods to overcome such difficulties

The ecological dynamics of pathogens have also been explored using models, including antimicrobial resistance

Economic outcomes were not considered in dynamic transmission models until 2011

Country of study

A number of studies (36%, 32 studies) did not specify a particular national setting. Of the publications that did; only three studies (3%) explored transmission of HCAI in lower and lower middle income countries

Methods employed for mathematical modelling of HCAIs

Stochastic vs. deterministic

The first HCAI models captured transmission dynamics in single wards using deterministic approaches

**Pathogen**

**Interventions studied**

**First published**

**References**

**MRSA**

Hand hygiene

1997

Antibiotic stewardship

1997

Isolation

1997

HCW cohorting

2002

Screening

2005

Decolonisation

2009

Patient cohorting

2007

Gown and glove use

2009

Other

2006

**VRE**

Hand hygiene

1998

Antibiotic stewardship

1999

Isolation

2004

HCW cohorting

1998

Screening

2004

Decolonisation

2007

Patient cohorting

2008

Environmental cleaning

2008

**
C. difficile
**

Other

2009

**ARB**

Hand hygiene

1997

Antibiotic stewardship

1997

Barrier precautions (i.e. not specified)

2000

**HCAI in general**

Hand hygiene

1999

Isolation

2005

HCW cohorting

2006

Screening

1999

Vaccination

2008

Barrier precautions (i.e. not specified)

2007

Patient cohorting

2005

Environmental cleaning

2007

Antibiotic prophylaxis

2007

Antibiotic stewardship

2008

HCW cohorting

2005

**HIV**

Sterilization of medical appliances

1999

**Influenza or ILI**

Vaccination

2008

Prophylaxis

2009

Other

2008

**Pertussis**

Vaccination

2009

**Rotavirus**

Hand hygiene

2011

HCW cohorting

2011

Vaccination

2011

**SARS**

Isolation

2007

Barrier precautions (i.e. not specified)

2005

**TB**

Isolation

2007

HIV treatment

2007

Air ventilation

2007

Facial mask

2007

Development of HCAI model methods used over time (1993–2011)

**Development of HCAI model methods used over time (1993–2011).** Application of key modelling characteristics and development over time.

Milestones of HCAI modelling

**Milestones of HCAI modelling.** Timeline listing new applications of mathematical models for HCAI and antimicrobial resistance over time as well as improvements of these models according to year of publication.

Compartmental vs. individual-based

Infectious disease models can have either an aggregate (or compartmental) structure (which tracks groups in the population) or an individual-based structure (which tracks individuals). The latter enables better incorporation of heterogeneity in patient characteristics such as patient demographics, contact patterns and disease history, but at the cost of increased computational burden. To date, most (73%; 70 studies) HCAI models have taken an aggregate approach, although the proportion of individual-based models has increased over time (Figure

Model fitting to data

Model parameter values can be based on existing studies, assumptions, or estimated directly from data

Uncertainty in model predictions

Infectious disease models are developed and informed using a combination of available evidence, for example on infection transmission, disease natural history and intervention effectiveness. As availability of such information is unlikely to be complete, mathematical models inherently include some degree of uncertainty. This uncertainty may relate to model parameter values, model structure (e.g. in terms of disease states incorporated and the relationship between them) or methodology used

Parameter uncertainty was investigated by 36% of the studies (35 publications). As Figure

Model validation

Model validation is rare in HCAI modelling. Ideally, a model should be validated by means of comparing the model predictions with observations from an alternative dataset than the one used for model fitting, although this is often difficult in practice. Four studies (5%) reported some kind of model validation based on at least two different data sets

Setting and interaction between settings

Mathematical models of HCAIs have primarily been set in a single ward (49%, 47 studies), with the intensive care unit (ICU) being the most frequent setting modelled (26%, 25 studies)

Discussion

Models of MRSA transmission dominate the literature, followed by VRE, although to a considerably lesser extent. Both have been the subject of national surveillance and infection control policies in a variety of developed countries

In terms of model methods, considerable changes can be identified over time. After the introduction of the first deterministic HCAI modelling study, inclusion of stochasticity has become common practice. The majority of the HCAI models evaluate infection control policies, for which sound model parameterisation and sensitivity analyses are required for reliable predictions. The use of more sophisticated methods for model parameterisation (e.g. MCMC) and uncertainty analysis has become increasingly common.

HCAI models have also increased in complexity regarding the settings modelled. Although the majority of the models have considered a single ward (often ICUs), the apparent emergence of transmission of typical HCAIs in the community, in particular of MRSA

This review has some limitations. First of all we have exclusively considered peer-reviewed publications in English. This might have resulted in a slight inaccuracy in our results, e.g. with regards to the modelling of particular pathogens in alternative national settings. We were exclusively interested in models exploring the patient-to-patient transmission of HCAI and antimicrobial resistance within healthcare settings (either directly, or mediated by healthcare workers and/or the healthcare environment). This has resulted in the exclusion of a higher number of models that elucidate the dynamics of antimicrobial resistance in its own right, which are summarised elsewhere

Compartmental models (which group individuals in classes) have predominated the field of HCAI modelling. The emergence of individual-based modelling allows for more realistic modelling of healthcare worker-patient contact (e.g. super spreading events) or incorporation of heterogeneity in transmission risk profiles of patients. However, these approaches are computationally far more intensive, are difficult to fit to data, and the inclusion of additional factors makes more demand on the data available. Detailed level data such as observed healthcare worker-patient contact collected for example via mote-based sensor networks, as has been done recently

Moreover, recent technological developments in microbiology have resulted in enhanced access to pathogen sequence data, which could help to further improve HCAI models. Such data are beginning to inform disease outbreaks e.g. of avian influenza A (H7N7)

Conclusions

Transmission models concerning HCAI have showed a general enhancement in complexity, but have been almost completely limited to high-income settings, and have strongly focused on MRSA transmission in hospital settings. Further improvements in the availability of data and statistical methods could enhance the insight gained from these models.

Abbreviations

ARB: Antimicrobial resistant bacteria; CRE: Cephalosporin-resistant Enterobacteriaceae; ESBL: Extended-spectrum beta-lactamases; HCAI: Healthcare-associated infections; ICU: Intensive care unit; ILI: Influenza-like illness; LHS: Latin Hybercube Sampling; LTCF: Long-term care facility; MCMC: Markov Chain Monte Carlo; MRSA: Methicillin-resistant

Competing interests

The authors declare that they have no competing interests.

Authors’ contributions

EvK developed the search strategy in collaboration with JR, and conducted a title-abstract screening, independent from a shared title-abstract screening by MJ, SD and WJE. Full text evaluation was conducted by EvK and in case of uncertainty, discussion took place with JR. EvK wrote the manuscript with significant contributions from the other authors. All authors have read and approved the final manuscript.

Acknowledgement

The authors are grateful to the referees for their valuable suggestions and advice. This work was supported by the Healthcare Infection Society.

Pre-publication history

The pre-publication history for this paper can be accessed here: