Transmission thresholds for the spread of infections in healthcare facilities

Abstract

Some infections may be sustained in the human population by persistent transmission among patients 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 high-risk infections. 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 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 long-term 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, R0 is 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.

Fig 1. Relationships between facility 𝐑0 and equilibrium clinical infection incidence with constant importation.

The curve was generated using formulas for Model 4, at values for the surveillance test frequency ranging from 0 to once per week and no pathogen reduction effect of the intervention. Other model parameters were set at the assumed and estimated values described in Section 3.3, fit to data from CPE in LTACHs. The points (circles) represent average surveillance intervals of, from left to right, one week, two weeks, one month, and no surveillance. Facility ${𝐑}_{\text{0}}$ was calculated using the formula in Section 3.2.4 with no decolonization, and we calculated infections per admission as the product of the mean length of stay, the per capita clinical detection rate, and the equilibrium prevalence of colonized, non-clinically detected patients, assuming a constant importation rates of 0.01% (solid), 0.1% (dashed), 1% (dotted), and 5% (dash-dot).

Fig 2. Effect of length-of-stay interventions on facility basic reproduction number.

Calculations of the facility reproduction number, ${𝐑}_{\text{0}}$, for Model 3 with the following fixed values calibrated to pre-intervention CRE data in long-term acute care hospitals (Table 3): transmission rate $\mathit{\beta }= \text{0}.\text{051}$ per day, clinical detection rate ${\mathit{\delta }}_{\text{c}}= \text{0}.\text{0084}$ per day, colonization clearance rate $\mathit{\gamma }=\text{1}/ \text{387}$ per day, and contact precaution effectiveness $\mathit{ϵ}=\text{0}.\text{5}$. Length of stay was governed by a 4-parameter mixed exponential–gamma distribution, and specific parameters were varied from the baseline values (Table 3) in a direction that decreased the overall mean length of stay from left-to-right in each of the sub-figures, while holding all other parameters constant. Upper-left: both the exponential rate parameter ${𝐫}_{\text{x}}$ and the gamma rate parameter ${𝐫}_{\text{g}}$ were simultaneously increased by the same factor from their baseline values. Upper-right: the exponential rate parameter ${𝐫}_{\text{x}}$ was increased from its baseline value. Lower-left: the gamma rate parameter ${𝐫}_{\text{g}}$ was increased from its baseline value. Lower-right: the fraction of patients following the exponential distribution ${𝐩}_{\text{x}}$ was decreased from its baseline value.

Fig 3. Scatterplot of facility basic reproduction number vs. length of stay (LOS) distribution statistics.

Calculations of the facility reproduction number, ${𝐑}_{\text{0}}$, for Model 3 with the following fixed values calibrated to pre-intervention CRE data in long-term acute care hospitals (Table 3): transmission rate $\mathit{\beta }=\text{0}.\text{051}$ per day, clinical detection rate ${\mathit{\delta }}_{\text{c}}=\text{0}.\text{0084}$ per day, colonization clearance rate $\mathit{\gamma }=\text{1}/ \text{387}$ per day, and contact precaution effectiveness $\mathit{ϵ}=\text{0}.\text{5}$. The dots represent ${𝐑}_{\text{0}}$ results for 1000 sets of values for each of the four parameters governing the mixed exponential–gamma length of stay distribution, drawn from four independent uniform distributions ranging from 60% to 140% of the calibrated values in Table 3. Each subplot displays the same 1000 ${𝐑}_{\text{0}}$ results, plotted against different statistics of the length of stay distribution for each set of length-of-stay parameters.