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A Mathematical Model Quantifying the Impact of Antibiotic Exposure and Other Interventions on the Endemic Prevalence of Vancomycin-Resistant Enterococci

  1. Erika M. C. D’Agata1,
  2. Glenn Webb2 and
  3. MaryAnn Horn2
  1. 1Division of Infectious Diseases, Beth Israel Deaconess Medical Center, Harvard Medical School, Boston, Massachusetts;
  2. 2Department of Mathematics, Vanderbilt University, Nashville, Tennessee
  1. Reprints or correspondence: Dr. Erika D’Agata, Beth Israel Deaconess Medical Center, Div. of Infectious Diseases, 330 Brookline Ave., East Campus Mailstop SL-435G, Boston, MA 02215 (edagata{at}bidmc.harvard.edu)
 
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Abstract

BackgroundMathematical modeling can be used to describe the interdependent and dynamic interactions that contribute to the transmission dynamics of vancomycin-resistant enterococci (VRE). A model was developed to quantify the contribution of antibiotic exposure and of other modifiable factors to the dissemination of VRE in the hospital setting

MethodsThe model consists of 4 compartments: patients colonized with VRE receiving and not receiving antibiotics and uncolonized patients receiving and not receiving antibiotics. A series of differential equations describe the movement between these compartments. Baseline parameter estimates were obtained from pharmacy, infection-control, and clinical databases

ResultsThe main predictions of this model are that (1) preventing the initiation or enhancing the discontinuation of unnecessary antimicrobial therapy will have a greater impact if it is targeted to patients who are not colonized with VRE; (2) increasing the number of patients harboring VRE at the time of hospital admission substantially increases the endemic prevalence of VRE; and (3) eliminating the influx of VRE results in the eradication of this pathogen from the hospital. A decrease in the endemic prevalence of VRE also occurs with a decrease in the length of hospital stay of colonized patients, increased hand hygiene compliance, and a lower ratio of health-care workers:patients

ConclusionThis mathematical model provides a framework to assist in targeting necessary interventions aimed at limiting the spread of VRE

Despite efforts to prevent the cross-transmission of vancomycin-resistant enterococci (VRE) between hospitalized patients, rates of vancomycin resistance among enterococci continue to increase [1]. This persistent increase may reflect an incomplete understanding of the complexities of the transmission dynamics of VRE and of the contribution of antibiotic exposure to the increase in both the likelihood of VRE acquisition and patient-to-patient spread [2–4]. Because classic epidemiological study designs cannot address the numerous interdependent and dynamic interactions that contribute to the dissemination of VRE, mathematical models have been developed [5–8]. These models use a series of differential equations that describe the complex interactions between patients and health-care workers (HCWs) that are involved in the transmission of VRE. Simulations can then be performed to determine the impact of specific interventions on the overall prevalence of VRE over time. Previous mathematical models have quantified the beneficial impact of several interventions—including surveillance cultures, patient cohorting, and improved hand hygiene compliance—in decreasing the prevalence of VRE [6–8]

We developed a mathematical model to address the impact of antibiotic exposure on the transmission dynamics of VRE. Specifically, we wanted to quantify the effects of preventing the initiation or enhancing the discontinuation of unnecessary antimicrobial therapy. The model consists of 2 patient populations in a tertiary-care center: those receiving antibiotics and those not receiving antibiotics. It was assumed that patients colonized with VRE who were receiving antibiotics were more likely to transmit VRE to other patients, given that antibiotic exposure increases quantities of VRE in stool and leads to a greater likelihood of skin and environmental contamination [2, 3, 9]. Simulations were then performed to quantify and compare the impact of starting antibiotics de novo or of discontinuing antibiotics in varying proportions of patients either colonized or uncolonized by VRE on the prevalence of VRE over time. Simulations were also performed to evaluate the impact of varying other important factors that contribute to the transmission of VRE, including the number of patients harboring VRE admitted to the hospital, the length of hospitalization of colonized patients, hand hygiene compliance, and the ratio of HCWs:patients

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Patients and Methods

Baseline modelThe model describes the transmission dynamics of VRE in all patients hospitalized in a 400-bed tertiary-care hospital. Patients were grouped into 2 populations: those receiving antibiotics and those not receiving antibiotics (1 and 0, respectively). In each population, patients may or may not have been colonized with VRE (c and u respectively). Thus, the model consists of 4 compartments: uncolonized patients receiving antibiotics (Pu1), uncolonized patients not receiving antibiotics (Pu0), colonized patients receiving antibiotics (Pc1), and colonized patients not receiving antibiotics (Pc0). The total number of hospitalized patients (Np) is equal to Pu0 + Pu1 + Pc0 + Pc1. There was bidirectional movement between the Pu0 and Pu1 compartments (antibiotics could be started or stopped in uncolonized patients) and between Pc0 and Pc1 (antibiotics could be started or stopped in colonized patients). However, it was assumed that patients receiving antibiotics could move from an uncolonized state to a colonized state but not the reverse. This assumption was based on the premise that the loss of VRE colonization requires an absence of antibiotic exposure [4, 10]. It was also assumed that patients who were not receiving antibiotics could move from a colonized state to an uncolonized state but not the reverse, because antibiotic exposure is a prerequisite for VRE colonization [11–14]. The importance of antibiotic exposure in VRE colonization has been reviewed by Donskey [4]. Movement between compartments reflected the proportion of patients in each group who were started receiving antibiotics (τ) or stopped receiving antibiotics (σ) (figure 1). These baseline estimates were obtained through a review of computerized pharmacy records for the year 2003

Figure 1
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Figure 1

Compartment model describing the transmission dynamics of vancomycin-resistant enterococci in a hospital setting between patients receiving and not receiving antibiotics. The following variables were used: P total no. of patients; u uncolonized state; c colonized state; 0, not receiving antibiotics; 1, receiving antibiotics; λ, no. of patients admitted to the hospital/day; γ, length of hospital stay; τ, no. of patients who started receiving antibiotics/day; σ, no. of patients who discontinued antibiotics/day; αp health-care worker (HCW) contact rate with patients; βp probability of patient colonization per HCW contact; η, hand hygiene compliance ρ, ratio of HCWs:patients; Hc/Np, fraction of contaminated HCWs

The model also incorporates the transmission of VRE between patients through contact with the contaminated hands of HCWs. The HCW contact rate per patient (αp) and hand hygiene compliance (η) during a 24-h period were extrapolated from periods of direct observation [15]. Approval for the observation of HCWs was obtained from Beth Israel Deaconess Medical Center’s Committee on Clinical Investigation. It was assumed that the probability of HCW hand contamination (βh) with VRE was greater from contact with colonized patients receiving antibiotics than from colonized patients not receiving antibiotics, given the strong correlation among antibiotic exposure, VRE density in stool, and skin contamination [2, 3]. To simplify the model, the contribution of contaminated clothing of HCWs and inanimate objects to the transmission of VRE was omitted

Patients could enter the hospital (Λ) in 1 of 4 states: colonized and either receiving or not receiving antibiotics and uncolonized and either receiving or not receiving antibiotics. These baseline values were obtained by a review of computerized infection-control records, which monitor the number of patients who are admitted to the hospital with a history of VRE, and of pharmacy records. Patients left each compartment after an average length of hospital stay (γ), for which values were obtained from the hospital administrative data (see Appendix)

Model simulationsSimulations were performed to quantify the impact of varying the value for (1) the number of colonized and uncolonized patients in whom antibiotics were started de novo, (2) the number of colonized and uncolonized patients who stopped receiving antibiotics, (3) the number of patients who were harboring VRE at the time of hospital admission, (4) the length hospitalization for colonized patients (γc), (5) hand hygiene compliance among HCWs, and (6) the ratio of HCWs:patients

R0 valueThe R0 value represents the number of patients who would be secondarily infected with VRE by a case patient at the beginning of an epidemic. The solution of this value would require the assumption of a steady state with no influx of either colonized or uncolonized patients into the hospital. Because the influx of patients colonized with VRE is an important parameter in the transmission dynamics of VRE in the hospital setting [16], a steady state cannot be assumed; therefore, an R0 value was not calculated

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Results

Baseline Model

According to the pharmacy, infection-control, and clinical databases, ∼30% of hospitalized patients/day received antibiotics; antibiotics were started de novo in 15% and 16% of uncolonized and colonized patients/day, respectively; and antibiotics were discontinued in 15% and 4% of uncolonized and colonized patients/day, respectively. According to the infection-control records, ∼1 patient harboring VRE/day (range, 0–5 patients/day) is admitted to the hospital. The average duration of hospitalization for colonized patients is 28 days. The average HCW:patient ratio is 1:4, with a hand hygiene compliance of 40%/patient contact. When these and other values listed in table 1 are used, the model projects an overall prevalence of VRE of 12% over time

Figure 2
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Figure 2

Model predictions of the prevalence of vancomycin-resistant enterococci (VRE) over time when varying the no. of patients who start receiving antibiotics de novo or who discontinue antibiotics, by colonization status, under the assumption of the baseline values listed in table 1

Figures 3
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Figures 3

A–D Model simulations describing the prevalence of vancomycin-resistant enterococci (VRE) over time when varying the no. of patients harboring VRE admitted to the hospital (A) the length of hospitalization in patients colonized with VRE (B) hand hygiene compliance (C) and the ratio of health-care workers (HCWs):patients (D). Baseline values are presented in table 1

Table 1
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Table 1

Baseline parameter values and estimates for the transmission of vancomycin-resistant enterococci in a hospital setting, for uncolonized and colonized patients

Model Simulations

Antibiotic exposureThe model predicts that changes in antibiotic exposure in uncolonized patients has a greater impact on the prevalence of VRE than do changes in antibiotic exposure in patients colonized with VRE. For example, in uncolonized patients, increasing the percentage of patients who start receiving antibiotics de novo from 15% to 20% to 30% increases the prevalence of VRE from 12% to 15% to 22%. In contrast, in colonized patients, an increase in the percentage of patients who start receiving antibiotics from 12% to 15% to 30% increases the prevalence of VRE from 11% to 12% to 13.5%. The model also predicts that the effect of increasing the percentage of colonized patients who start receiving antibiotics de novo to >15% was marginal, in that the prevalence of VRE reached a plateau of 12%–13%. In contrast, increasing the percentage of uncolonized patients who start receiving antibiotics de novo to >15% resulted in an exponential increase in the prevalence of VRE (figure 2)

The model also projects that stopping antibiotics in uncolonized patients has a substantial effect on the overall prevalence of VRE. Under the assumption that, in uncolonized patients, 15%/day have antibiotics discontinued at baseline, the model demonstrates that, below this threshold percentage, an increase in the number of patients who do not stop receiving antibiotics substantially increases the prevalence of VRE only in uncolonized patients. For example, if the percentage of uncolonized patients in whom antibiotics are not discontinued is decreased from 15% to 10% to 5%, the prevalence of VRE increases from 12% to 14% to 21%. In contrast, similar decreases in the percentage of colonized patients in whom antibiotics are not discontinued increases the prevalence to only 13% (figure 2)

Number of patients harboring VRE entering the hospital Figure 3A shows the effect of increasing the number of patients colonized with VRE who are admitted to the hospital. The model predicts that increasing the number of colonized patients from 1 to 2 to 3 per day would increase the prevalence of VRE from 12% to 21% to 28%. The model also projects that eliminating this influx of VRE into the hospital (0 patients harboring VRE at admission/day) is the only intervention that would eradicate VRE from the hospital setting

Other Simulations

Figure 3B–3D describes the impact of varying the length of hospitalization for colonized patients, hand hygiene compliance, and the ratio of HCWs:patients on the overall prevalence of VRE

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Discussion

The present mathematical model describes and quantifies the impact of several interventions aimed at decreasing the prevalence of VRE in a hospital setting and predicts that (1) preventing the initiation or enhancing the discontinuation of unnecessary antimicrobial therapy has a greater impact when it is targeted to patients who are not colonized with VRE than when it is targeted to patients colonized with VRE; (2) preventing the influx of VRE into the hospital from patients already harboring VRE at the time of admission decreases the prevalence of VRE substantially and, if this is reduced to zero, eliminates VRE entirely from the hospital setting; and (3) prolonging the duration of hospitalization of colonized patients increases the prevalence of VRE substantially. The model also confirms the importance of improved hand hygiene compliance and a lower ratio of HCWs:patients in limiting the dissemination of VRE [6–8]

Antimicrobial exposure plays a key role in the transmission dynamics of VRE. The selective pressure exerted by antimicrobials on the gastrointestinal flora promotes colonization with VRE [4, 15]. Antimicrobial exposure also promotes the overgrowth of VRE, which leads to substantially more skin and environmental contamination and an increased likelihood of VRE cross-transmission to other patients [2, 3, 9]. The present mathematical model incorporates these 2 important effects of antimicrobial exposure by increasing the likelihood of the acquisition of VRE by uncolonized patients receiving antibiotics, compared with patients not receiving antibiotics, and increasing the likelihood of the dissemination of VRE or the contamination of HCWs for colonized patients receiving antibiotics, compared with patients not receiving antibiotics. The model predicts that improved antibiotic use—including preventing the initiation of unnecessary antimicrobial therapy or enhancing the discontinuation of unnecessary antimicrobial therapy—would have a greater impact if it were targeted to patients who are not colonized with VRE. The greater impact of antibiotic exposure in uncolonized patients, compared with colonized patients, is explained by the smaller proportion of hospitalized patients who were colonized. The model also predicts that the prevalence of VRE will increase substantially if the percentage of uncolonized patients who start receiving antibiotics de novo increases to above a threshold of 15% or if the percentage of uncolonized patients who do not stop receiving antibiotics decreases to <15%

The model quantifies the marked impact on the prevalence of VRE of increasing the number of patients already harboring VRE who are admitted to the hospital: an increase from 1 to 2 to 3 colonized patients/day would ultimately increase the prevalence of VRE from 12% to 21% to 30%. Because the number of patients harboring VRE at the time of hospital admission is rapidly increasing [16], the detection of these unrecognized reservoirs of VRE at the time of hospital admission is of paramount importance. Surveillance cultures for VRE performed at the time of hospital admission could identify colonized patients who would then be placed on contact precautions to limit the dissemination of VRE to other patients. Surveillance cultures to detect colonization by VRE in high-risk wards, outpatient dialysis units, and at the time of hospital admission have shown a substantial benefit in reducing the transmission of VRE and are cost-effective [7, 8, 17–19]. A simple prediction rule has been developed that identifies patients at a high risk of harboring VRE at the time of hospital admission [16]. Implementation of this rule would target surveillance cultures to a subset of patients at the time of hospital admission who are at a high risk of VRE colonization and would thereby limit the necessary additional resources required for VRE screening cultures [16]

The effect of varying the length of hospitalization of colonized patients was also analyzed, and its impact on increasing the prevalence of VRE was quantified. Because colonized patients are the main reservoirs of VRE in the hospital setting, prolonged hospitalizations of colonized patients would lead to more-frequent opportunities for the dissemination of VRE. Although the length of hospitalization cannot be substantially modified, this factor was used as a surrogate for the theoretical possibility of eradicating VRE from the gastrointestinal tract or selective decontamination by pharmaceutical agents [4, 20]. Future studies may demonstrate the benefit of a pharmacological approach to infection control whereby the administration of antimicrobials, which eradicate or suppress VRE colonization, could be used to eliminate the patient reservoir of VRE at the time of admission or during hospitalization. Concern regarding the overgrowth of gram-negative flora when eliminating VRE and other gram-positive bacteria from the gastrointestinal tract, however, has been raised [4]

The strength of a mathematical model’s conclusions reflects the validity of the model’s assumptions and the baseline parameters. In the present model, the assumptions of VRE transmission between patients and HCWs were based on patterns that have been defined in numerous epidemiological studies of VRE transmission [13, 18, 21–23], and baseline parameters were obtained from infection-control, pharmacy, and clinical databases. Several values were estimated, including the probability of HCW contamination per contact with a colonized patient and the probability of patient colonization from a contact with a contaminated HCW. Given the difficulties in quantifying these values, estimates used in previous mathematical models of VRE transmission were adopted [6, 8]. To simplify the model, we omitted the contribution of environmental contamination in the dissemination of VRE. Although the importance of contaminated inanimate objects in the spread of antimicrobial-resistant bacteria has been demonstrated, the omission of this factor should not affect the overall conclusions of the model [3, 9, 24]

The implementation of effective preventive measures aimed at limiting the dissemination of VRE in hospitalized patients requires a thorough understanding of the transmission dynamics of VRE. Quantifying the contribution of each of the numerous factors involved in the dissemination of VRE allows a greater emphasis on those preventive measures that are associated with the greatest reduction in the risk of transmission of VRE. The present model quantifies the benefit of preventing the initiation and enhancing the discontinuation of unnecessary antimicrobial therapy and the importance of surveillance cultures in detecting patients harboring VRE at the time of hospital admission in impeding the persistent increase in the number of hospitalized patients who harbor VRE

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Footnotes

  • ↵Potential conflict of interest: E.M.C.D. has been a consultant and has received research funding from Genome Therapeutics

    Financial support: Genome Therapeutics

  • Received November 29, 2004.
  • Accepted June 14, 2005.
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