The role of intra and inter-hospital patient transfer in the dissemination of heathcare-associated multidrug-resistant pathogens

Healthcare-associated infections cause significant patient morbidity and mortality, and contribute to growing healthcare costs, whose effects may be felt most strongly in developing countries. Active surveillance systems, hospital staff compliance, including hand hygiene, and a rational use of antimicrobials are among the important measures to mitigate the spread of healthcare-associated infection within and between hospitals. Klebsiella pneumoniae is an important human pathogen that can spread in hospital settings, with some forms exhibiting drug resistance, including resistance to the carbapenem class of antibiotics, the drugs of last resort for such infections. Focusing on the role of patient movement within and between hospitals on the transmission and incidence of enterobacteria producing the K. pneumoniae Carbapenemase (KPC, an enzyme that inactivates several antimicrobials), we developed a metapopulation model where the connections among hospitals are made using a theoretical hospital network based on Brazilian hospital sizes and locations. The pathogen reproductive number, R0 that measures the average number of new infections caused by a single infectious individual, was calculated in different scenarios defined by both the links between hospital environments (regular wards and intensive care units) and between different hospitals (patient transfer). Numerical simulation was used to illustrate the infection dynamics in this set of scenarios. The sensitivity of R0 to model input parameters, such as hospital connectivity and patient-hospital staff contact rates was also established, highlighting the differential importance of factors amenable to change on pathogen transmission and control.


Motivation
Hospital-acquired infections (HAI) are mainly caused by opportunistic bacteria resistant to antibiotics. Ninety percent of HAIs occur in Intensive Care Units (severity of illness of patients, the extensive use of wide-spectrum antibiotics and invasive procedures).
These infections increase patient morbidity and mortality, and impose healthcare costs.
Transmission occurs at the level of single hospital, and at regional, and national level by interhospital patient transfers.
In Europe and North America between 5% and 10% of all hospitalizations result in HAI while in other countries this percentage is up to 40%.

Objective
Focusing on the role of patient movement within and between hospitals on the transmission and incidence of enterobacteria producing the Klebsiella pneumoniae Carbapenemase (KPC), we developed a metapopulation model where the connections among hospitals are made using a theoretical hospital network based on Brazilian hospital sizes and locations.
The pathogen reproductive number, R 0 was calculated in different scenarios defined by both the links between hospital environments (regular wards and intensive care units) and between different hospitals (patient transfer).
The sensitivity of R 0 to model input parameters, such as hospital connectivity and patient-hospital staff contact rates was also established, highlighting the differential importance of factors amenable to change on pathogen transmission and control.
Hospitals can be classified as a source or a sink of infection based on its R 0 value. Can the concept of source-sink dynamics be used to define strategies of control?

Hospital network (2011)
Due to the lack of information about patient transfers among hospitals, we built a theoretical undirected, unweighted network using the known location and size (estimated by the number of hospital beds) of Brazilian hospitals. We used the ArcGIS software to geocode hospital locations and to measure the pairwise distance between all hospitals.
We excluded hospitals with incomplete data and those with less then ten beds.
Each hospital is connected to its eight nearest same-/higher-level hospitals (level 1 hospitals are connected only to higher-level hospitals).
The resulting network comprises 6214 hospitals classified as general hospital nonspecialized units (only regular wards, total of 4575), or mixed hospitals (both regular wards and ICU facilities, total of 1639).

Multi-patch model (2002)
Each patch represents a hospital, and connections between two patches is due to patient transfers.
We assume that a hospital can have two distinct environments, differing by the infection-acquiring risk, which are the regular ward and the ICU facility, and the healthcare workers (HCW) act as the vectors of pathogen transmission.
The model assumptions are: (i) KPC is not endemic in the Brazilian population at large, but is present in hospitals. Consequently, there are no entries of colonized individuals into hospitals; (ii) Patients are moved between the two hospital environments, the ICU and regular wards; (iii) Patients must pass through a regular ward before being discharged from the hospital; (iv) Only ICU patients have a significant mortality rate; (v) Once colonized, a patient remains in this epidemiological state until leaving the hospital; (vi) Transfers among hospitals are given by the Brazilian hospital network; (vii) Workers (hospital staff) can revert from colonized to non-colonized state due to hygiene practices.

ODE system
Variables are healthcare workers, and patients; both susceptible or colonized Each environment has its own healthcare staff;

Parameter estimation
Using the Brazilian health ministry website, we computed the number of admissions in the Brazilian healthcare system in the year 2016. This number was divided by 365 and by the total number of available hospital beds in Brazil. We considered that hospitals have a daily patient admission rate proportional to their capacity.
The number of HCW was estimated using the Brazilian resolution. Healthcare-work shifts operate as eight-hour rotations and we assumed that hand-washing frequency has the same range that describes the contact frequency.
The rates of transfer between ICU and regular wards were estimated using data from the Medical School of Botucatu (FMB-UNESP) obtained from 2015 to 2016. This data set contains information about patient admission date, movement between ICU and regular wards, and final date (including both discharges and deaths) of 200 patients.

Scenario I -Spreading of a localized infection
No coupling between the ICU and regular wards in a single hospital, and no patient is transferred among hospitals. The DFE is given by and the threshold, R 1 , can be obtained through the next generation matrix. Therefore, where If R 1 < 1 the infection cannot persist in the hospital. Moreover, if both R P1 and R U1 are greater than 1 the infection is present in the entire hospital, otherwise if R P1 > 1 and R U1 < 1 (R P1 < 1 and R U1 > 1) it is present just in the regular ward (ICU) environment.
Both thresholds have similar expressions to those derived from mathematical models of vector-borne diseases, except that the ratio between the two populations (host and vector) is reversed when compared to classical vector-borne disease models.
This happens because of the assumption that each patient requires a fixed number of contacts per day; therefore, increasing the number of HCW, the number of contacts that each HCW will perform decreases, which reduces infection transmission between patients and HCW. Moreover, it implies that for HAI transmission, increasing HCW (vectors for transmission) decreases R 1 .
The literature points out that decreased staffing (understaffing) is one of the major drivers of transmission of multidrug-resistant bacteria in hospitals.

Scenario II -Individuals are transferring between ICU and regular ward
Consider the transmission dynamics in a single hospital. The DFE is given by for which If R 2 > 1 the infection persists in the hospital, otherwise it dies out. In contrast to scenario I, the disease is either present in both hospital environments or completely absent.
Note that δ UP δ PU → 0 =⇒ R 2 ∼ max{R U2 , R P2 }. When both parameters are zero, the environments are isolated and we recover the result obtained in scenario I.
On the other hand, when δ UP → ∞ and δ PU → ∞ =⇒ R 2 ∼ R U2 + R P2 . In this case, intra-hospital transfer rates are so high that we cannot distinguish between the two environments.
The effect of patient transfer on infection dynamics is non-trivial, including the phenomenon whereby increasing the transfer rates can promote extinction or persistence of infection.
Overall the transmission rates and the parameters pertaining to the ICU environment are most influential for transmission and persistence of the infection; with b U β U , W U , µ P and ν emerging as the most important parameters in this scenario.

Scenario III -Coupling among hospitals
In this more extended system, it is convenient to use a vectorial notation to expedite an explicit expression for the epidemic threshold.
Using the next generation operator, an explicit equation for R 3 that be obtained; R 3 is calculated numerically. If R 3 > 1 infection transmission persists in the hospital, otherwise it stops. This scenario is explored through a sensitivity analysis and the concept of "sourcesink" dynamics, which assumes that transmission in some environments cannot be sustained ("sink") without the arrival of new infected individuals to re-establish a chain of transmission ("source").
Each hospital was defined as "source" or "sink" based on its R 0 (threshold) value, which measure its ability to maintain transmission alone; a "source" hospital has R 0 > 1 and a "sink" hospital has R 0 < 1.

Sensitivity analysis, R 3 (control of the infection)
For β = 0.001, the order of importance is λ, τ , and δ PU ; the parameter δ UP was assigned as unimportant (left). However, when β was increased to 0.1, δ UP was assigned as important, even more so than τ (right). The hypothesis is that the amount of sources (or sinks) in the system changes the order of importance of the parameters.  When β increases, the parameter δ UP becomes important and negatively influences R 3 , because disease prevalence is higher in the ICU sector compared to regular wards.
The coupling between the hospitals, given by the parameter τ , may decrease or increase the R 3 value of the network, when compared with the individual values obtained for each hospital in the network.
Given that the number of HCW in each hospital is fixed, the most important parameter for control was a hygiene measure given by the parameter λ.
In the case of Brazil, the transfer rate among hospitals tended to decrease R 3 . This is likely because most hospitals in the network (4575/6214) have only regular wards (referral and counter-referral system).

Conclusion
Overall, our results suggest that a relatively high number of HCW per patient, along with healthcare compliance with hygiene are the key parameters to control the dissemination of HAIs.
Identifying the hospitals in the network that act as sources of infection, and determining the location inside a hospital where the incidence of infection is high can help to optimize control efforts. In this context, the referral and counter-referral system is a good strategy to reduce infection prevalence.
Patient movement between wards in a hospital or between hospitals should be evaluated based on HAI prevalence, underscoring the importance of a local and national active surveillance system.
Spatial variation in hospital sizes, presence or absence of an ICU, degree of connectivity, and inter-hospital transfer rate are ingredients that may promote source-sink dynamics at a regional and national scale.