Multivariate Markov Process Models for the Transmission of Methicillin‐Resistant Staphylococcus Aureus in a Hospital Ward

Methicillin-resistant Staphylococcus Aureus (MRSA) is a pathogen that continues to be of major concern in hospitals. We develop models and computational schemes based on observed weekly incidence data to estimate MRSA transmission parameters. We extend the deterministic model of McBryde, Pettitt, and McElwain (2007, Journal of Theoretical Biology 245, 470-481) involving an underlying population of MRSA colonized patients and health-care workers that describes, among other processes, transmission between uncolonized patients and colonized health-care workers and vice versa. We develop new bivariate and trivariate Markov models to include incidence so that estimated transmission rates can be based directly on new colonizations rather than indirectly on prevalence. Imperfect sensitivity of pathogen detection is modeled using a hidden Markov process. The advantages of our approach include (i) a discrete valued assumption for the number of colonized health-care workers, (ii) two transmission parameters can be incorporated into the likelihood, (iii) the likelihood depends on the number of new cases to improve precision of inference, (iv) individual patient records are not required, and (v) the possibility of imperfect detection of colonization is incorporated. We compare our approach with that used by McBryde et al. (2007) based on an approximation that eliminates the health-care workers from the model, uses Markov chain Monte Carlo and individual patient data. We apply these models to MRSA colonization data collected in a small intensive care unit at the Princess Alexandra Hospital, Brisbane, Australia.