# Transmission thresholds for the spread of infections in healthcare facilities

## TL;DR

This paper studies how infections spread in healthcare facilities and introduces a new formula to calculate the basic reproduction number R0, which helps determine if an outbreak can be sustained and how interventions can reduce it.

## Contribution

The paper provides a novel formula for R0 in healthcare facilities and shows how statistical properties like patient stay duration affect outbreak potential.

## Key findings

- R0 was estimated at 1.24 for carbapenemase-producing Enterobacteriaceae in long-term acute-care hospitals before intervention.
- Weekly surveillance with transmission reduction could lower R0 to 0.85, potentially preventing outbreaks.
- Reducing the mean length of stay alone may not reduce R0 if the variance-to-mean ratio remains unchanged.

## 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.

The spread of infectious diseases between patients admitted to the same healthcare facility can cause large outbreaks of dangerous organisms such as bacteria resistant to available antibiotic treatments. One way to quantify facility transmission is with the basic reproduction number, R0. When a facility patient acquires the organism, R0 is the average number of onward transmissions from that patient, when all other patients are susceptible. There is an important threshold effect at R0=1: when R0<1, a single introduction is unlikely to set off a long-lasting outbreak, but if R0>1, a continual chain of transmissions stemming from one introduction is possible. We provide a novel formula for R0 specific to healthcare facilities and exhibiting this threshold effect. We show that R0>1 likely occurred in facilities with high rates of drug-resistant bacterial infections, and we provide nuanced insights into intervention efforts to push R0<1 in those facilities. Our formulas reveal that R0 depends on statistical properties of healthcare facilities that are underappreciated for their epidemiological importance, such as the variance of patient stay duration. Our publicly available software allows other researchers to analyze models with customizable facility and disease properties and design intervention strategies for efficient reduction of facility outbreak risk.