Transmission thresholds for the spread of infections in healthcare facilities

Some infections may be sustained in the human population by persistent transmission among patients clustered in healthcare facilities, including patients colonized with multi-drug-resistant organisms posing a major health threat. A nuanced understanding of facility characteristics that contribute to crossing a threshold for self-sustaining outbreak potential may be crucial to designing efficient interventions for lowering regional disease burden and preventing infections among high-risk patients. Using a mathematical model, we define the facility basic reproduction number R0, where a single facility can sustain an outbreak without ongoing importation under the threshold condition R0 > 1. We define R0 for a general model with heterogeneous patient states of susceptibility and transmissibility and with generic length-of-stay assumptions, and we provide a software package for numerical calculation of user-defined examples. We estimate R0 using published data for carbapenemase-producing Enterobacteriaceae (CPE) in longterm acute-care hospitals (LTACHs) and the effects of interventions on R0, including surveillance, pathogen reduction treatments, and length-of-stay reduction. In a simple model, R0is directly proportional to the sum of the mean and variance-to-mean ratio of the length-of-stay distribution. In intervention models, R0 depends on the moment-generating function of the length-of-stay distribution. From the CPE data, we estimated R0 = 1.24 (95% CI: 1.04, 1.45) prior to intervention. Weekly surveillance with 50% transmission reduction of detected patients alone could have reduced R0 to 0.85 (0.72, 0.98), with additional reduction if detected patients could be decolonized. Reducing the mean length of stay does not necessarily reduce R0 if the variance-to-mean ratio is not also reduced. We conclude that R0 >1 conditions plausibly exist in LTACHs, where CPE outbreaks could be sustained by patients who acquire colonization and subsequently transmit to other patients during the same hospital stay. Our findings illuminate epidemiological mechanisms producing those conditions and their relationship to interventions that could efficiently improve population health.