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Mathematical and statistical modelling of infectious diseases in hospitals

McBryde, Emma Sue (2006) Mathematical and statistical modelling of infectious diseases in hospitals. PhD by Publication, Queensland University of Technology.

Abstract

Antibiotic resistant pathogens, such as methicillin-resistant Staphylococcus aureus (MRSA), and vancomycin-resistant enterococci (VRE), are an increasing burden on healthcare systems. Hospital acquired infections with these organisms leads to higher morbidity and mortality compared with the sensitive strains of the same species and both VRE and MRSA are on the rise worldwide including in Australian hospitals. Emerging community infectious diseases are also having an impact on hospitals. The Severe Acute Respiratory Syndrome virus (SARS Co-V) was noted for its propensity to spread throughout hospitals, and was contained largely through social distancing interventions including hospital isolation. A detailed understanding of the transmission of these and other emerging pathogens is crucial for their containment.

The statistical inference and mathematical models used in this thesis aim to improve understanding of pathogen transmission by estimating the transmission rates of contagions and predicting the impact of interventions. Datasets used for these studies come from the Princess Alexandra Hospital in Brisbane, Australia and Shanxi province, mainland China.

Epidemiological data on infection outbreaks are challenging to analyse due to the censored nature of infection transmission events. Most datasets record the time on symptom onset, but the transmission time is not observable. There are many ways of managing censored data, in this study we use Bayesian inference, with transmission times incorporated into the augmented dataset as latent variables. Hospital infection surveillance data is often much less detailed that data collected for epidemiological studies, often consisting of serial incidence or prevalence of patient colonisation with a resistant pathogen without individual patient event histories. Despite the lack of detailed data, transmission characteristics can be inferred from such a dataset using structured HiddenMarkovModels (HMMs).

Each new transmission in an epidemic increases the infection pressure on those remaining susceptible, hence infection outbreak data are serially dependent. Statistical methods that assume independence of infection events are misleading and prone to over-estimating the impact of infection control interventions. Structured mathematical models that include transmission pressure are essential. Mathematical models can also give insights into the potential impact of interventions. The complex interaction of different infection control strategies, and their likely impact on transmission can be predicted using mathematical models.

This dissertation uses modified or novel mathematical models that are specific to the pathogen and dataset being analysed. The first study estimates MRSA transmission in an Intensive Care Unit, using a structured four compartment model, Bayesian inference and a piecewise hazard methods. The model predicts the impact of interventions, such as changes to staff/patient ratios, ward size and decolonisation. A comparison of results of the stochastic and deterministic model is made and reason for differences given. The second study constructs a Hidden Markov Model to describe longitudinal data on weekly VRE prevalence. Transmission is assumed to be either from patient to patient cross-transmission or sporadic (independent of cross-transmission) and parameters for each mode of acquisition are estimated from the data. The third study develops a new model with a compartment representing an environmental reservoir. Parameters for the model are gathered from literature sources and the implications of the environmental reservoir are explored. The fourth study uses a modified Susceptible-Exposed-Infectious-Removed (SEIR) model to analyse data from a SARS outbreak in Shanxi province, China. Infectivity is determined before and after interventions as well as separately for hospitalised and community symptomatic SARS cases. Model diagnostics including sensitivity analysis, model comparison and bootstrapping are implemented.

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ID Code: 16330
Item Type: QUT Thesis (PhD by Publication)
Supervisor: McElwain, Donald, Pettitt, Anthony, & Whitby, Michael
Additional Information: Recipient of 2006 Outstanding Doctoral Thesis Award
Keywords: Bayesian inference, epidemic modelling, environmental reservoir, hiddenMarkov models, infectious diseases, mathematical modelling, methicillin resistant Staphylococcus aureus (MRSA), severe acute respiratory syndrome (SARS), statistical modelling, stochastic processes, vancomycin resistant enterococci (VRE), epidemiology, public health, infectious disease, ODTA
Divisions: Past > QUT Faculties & Divisions > Faculty of Science and Technology
Past > Schools > Mathematical Sciences
Department: Faculty of Science
Institution: Queensland University of Technology
Copyright Owner: Copyright Emma Sue McBryde
Deposited On: 03 Dec 2008 14:01
Last Modified: 17 Jun 2013 16:10

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