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

Abstract

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 in£uence 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 di¡erent 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 de¢ned country. The spread of methicillin resistant Staphylococcus aureus (MRSA) in England and Wales provides a template for model construction and analysis. The ¢nal 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 ¢tted 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.

Persistent colonization and the spread of antibiotic resistance in nosocomial pathogens: Resistance is a regional problem

“…If the LOS differs among groups, S j for a subpopulation involves averaging (see Appendix). Self-sustaining sources with rapid turnover may also play the role of superspreaders (20,24).…”

“…We have developed mathematical models with multiple institutions connected by patient movement; such models are called ''structured'' populations or ''metapopulations.'' Thus, we are developing epidemiological models (20,21,24) focused specifically on the consequences of persistent colonization and population structure, applying existing theory for structured populations (20,(24)(25)(26)(27).…”

Screening strategies in surveillance and control of methicillin-resistant Staphylococcus aureus (MRSA)

“…Whereas stochastic models define movements of individuals to be chance events occurring at random time-intervals determined by the model parameters, meaning the outcome may be different for different simulation runs. There have been a number of previous models looking specifically at nosocomial infection transmission dynamics [10][11][12][13][14][15][16][17][18][19]. This work builds on those studies, particularly those by Cooper et al [4,18,19] which use stochastic models to explore the spread of nosocomial pathogens.…”

“…This requires an understanding of underlying processes involved [13] and helps to identify areas in which more precise information is needed [11].…”

Of Models and Methods: Our Analytic Armamentarium Applied to Methicillin-Resistant Staphylococcus aureus

“…Following an earlier model of Austin and Anderson, Raboud et al allowed patients to exist in MRSA-colonized or MRSA-uncolonized states. 18 In this model, "colonization" referred to either colonization or infection. Similarly, HCWs were assigned to either uncolo-nized or transiently colonized states; transitions between states were stochastic events.…”