Review
Mathematical modelling: a tool for hospital infection control

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Summary

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.

Introduction

Health-care-associated infections are characterised by pathology related to the presence of infectious agents or their products as a result of exposure to health-care procedures. Among other transmissible agents (fungi, viruses, parasites, prions, etc), health-care-associated infections are often caused by bacteria, which have frequently acquired resistance to one or more antimicrobial agent. Importantly, these bacteria have the ability to colonise human beings for prolonged periods, and colonised patients may disseminate these nosocomial pathogens both during and after their hospital stay. Any means to control health-care-associated infections will need to adapt to the changing nature of medicine and health-care delivery and demand a thorough understanding of the underlying dynamics of health-care-associated infections with respect to their ecology, epidemiology, and economic ramifications. Best practice in this modern sense means adopting evidence-based and cost-effective methods. Mathematical models help identify factors responsible for observed patterns of occurrence and may provide theoretical guidelines for the design of efficient countermeasures. The purpose of this review is to explain recent quantitative models that describe the dynamics of health-care-associated infections in mathematical terms to a broader audience of professionals in health care, infection control, and health system administration.

Most models that describe the transmission dynamics of nosocomial pathogens divide the host population in the community or hospital into compartments of individuals who are either susceptible to colonisation or infection, or colonised or infected (figure).1 These compartment models make specific assumptions about the transmission process of bacteria between susceptible and colonised patients (either infected or asymptomatic carriers). Although some of these compartment models describe the ecological consequences of antimicrobial consumption on the competition between susceptible and resistant bacterial strains, and may thus be of interest to prescribers,6, 7, 8, 9, 10, 11 we concentrate on epidemiological models, which investigate the transmission of resistant pathogens in the context of institutional settings and that have direct implications on physical infection control strategies—eg, contact isolation, cohorting, hand hygiene, and patient referral practices.

Section snippets

Mathematical models in hospital epidemiology

Mathematical models have been widely used in quantitative infectious diseases epidemiology—eg, as tools to estimate the demographic effect of HIV in different populations, for decision support in vaccination policy, to predict the usefulness of control measures for vector-borne diseases, or the global spread of respiratory tract infections by international travel.1, 12, 13, 14, 15 Their contribution to hospital epidemiology has been rather recent. Before we discuss in more detail original

Single ward models

The mathematical models first published for hospital epidemiology were concerned with the transmission dynamics between patients in a single hospital ward.2, 3, 16, 21 Although deterministic models were an obvious starting point16, 21 it was quickly understood that, due to the typically small number of patients in single wards such as intensive care units with ten to 20 beds, chance or stochastic effects will be of importance.2, 3, 4

Two papers focus on stochastic effects (panel).2, 3 Both use a

Single hospital and community studies

Based on a systematic review of isolation policies in hospital management of MRSA, the first comprehensive hospital-community model was published by Cooper and colleagues.5, 17 The model set out to determine the long-term effects on MRSA prevalence when taking admission and discharge practices of MRSA patients into account. In a second step, the effect of introducing a contained isolation ward on the spread of MRSA in hospital and community was explored (figure, B). The resulting model explains

Models including multiple hospitals and communities

Smith and colleagues18 elegantly extended previous models by considering an entire health-care collective consisting of a finite number of subpopulations in hospitals, long-term care facilities, and the community served by these institutions (figure, C). In this metapopulation model, individuals move at certain rates between subpopulations that differ with respect to their composition, length of stay, and the frequency of transmission. This approach allows the study of the influence of core

Mathematical models for epidemiology: strengths and limitations

There is no doubt that the value of “classic” epidemiological investigations lies in its “quasi-experimental” nature, which allows assessment of the importance of certain variables under real world conditions. For example, the effect of a risk factor on a particular outcome can be measured. The quantity that best explains the observed variation of the outcome is the parameter characterising this relation.

The mathematical compartment models described here permit purely theoretical

Conclusions

Mathematical models, although fraught with simplifying assumptions, have the capacity to provide an insight into the forces that drive the epidemiology of health-care-associated infections and antimicrobial resistance in hospitals and communities. The past 5 years have seen a steady evolution and improvement of mathematical models that are able to describe, quantify, and capture the dynamics of transmission and spread of pathogens that can cause health-care-associated infections, most of which

Search strategy and selection criteria

Relevant publications and studies were identified by searches in PubMed and ISI Web of Science taking into account the bibliographies of all identified publications. Search terms were “mathematical” and/or “model” or “transmission dynamics” or “game theory” and (“hospital” or “health-care-associated” or “nosocomial” or “resistance” or “infection control”). Articles dealing with ecological considerations such as competition between antibiotic-sensitive and antibiotic-resisistant pathogens

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