Assessing the effect of patient screening and isolation on curtailing Clostridium difficile infection in hospital settings

Clinical studies demonstrate that a significant fraction of colonized patients remain infectious and can transmit the bacterium with no apparent symptoms [12, 14, 21]. These individuals may develop immune responses against C. difficile [14, 21], and we assumed that only colonized patients without immune responses develop clinical symptoms. It is well documented that the use of antibiotics increases susceptibility to colonization of C. difficile, as a result of damage to gut flora [14, 22, 23]. High rates of treatment failure for the management of CDI have been reported [14, 24, 25], with the possibility of recurrence even after effective treatment [26, 27]. We considered timelines for detecting colonized patients in two types of laboratory diagnosis methods including (i) the real-time polymerase chain reaction (PCR), and (ii) other tests of enzyme immunoassays, stool culture, and nucleic acid amplification [28‐30]. The average time to reportable results for rapid PCR (about 1.5 h) is significantly shorter compared to other testing assays that generally range from 1 to 3 days [28, 31, 32].

In order to develop the general framework of the model, we divided the population in a single ward into several compartments, including the classes of individuals who are susceptible and colonized. We further divided susceptible individuals into two main categories: those who are currently receiving antibiotic treatment for the management of infections other than CDI, with possible damage to their gut flora and increased risk of C. difficile colonization (S ₊); and those without recent exposure to antibiotic treatment (S ₋). We considered a transition between the two susceptible classes based on the rates of antibiotic treatment and recovery from damaged gut flora. A fraction of colonized individuals will mount immune responses against C. difficile and move to the class C ⁺; the remaining will enter the class C ⁻ without developing immune responses, and will progress to symptomatic disease (I). Both C ⁺ and C ⁻ comprised of colonized patients who are asymptomatically infectious. Patients with clinical symptoms are diagnosed and isolated. We assumed that patients with C. difficile symptoms under treatment are not discharged from the hospital prior to the resolution of their symptoms. Successful treatment of symptomatic CDI will lead to the resolution of symptoms and full recovery. The schematic model diagram for the dynamics of infection and patient screening is shown in Fig. 1.

Recognizing the importance of asymptomatic carriers in the hospital transmission of CDI [14, 20], we extended the main structure to include screening of patients at the time of admission, and in-hospital patients. A fraction of patients at the time of hospital admission will be screened and isolated if diagnosed with colonization of C. difficile, including patients with apparent symptoms (Additional file 1: Figure S1). For diagnosis using PCR testing method, we omitted the short time-interval (approximately 1.5–2 h [31]) prior to the release of laboratory results. We therefore introduced two classes of patients who are isolated and treated upon screening, based on whether they develop immune responses (\( {C}_T^{+} \)) or not (\( {C}_T^{-} \)). For diagnosis using other testing methods, we accounted for the delay between the time of sample collection and the time when laboratory results are released. Considering such a time delay, we introduced two additional classes of patients under screening with immune responses (\( {D}_T^{+} \)) and without immune responses (\( {D}_T^{-} \)). We assumed that during the screening period before the laboratory results are released, patients are neither isolated nor treated for C. difficile [13]. The transition of these patients to \( {C}_T^{+} \) and \( {C}_T^{-} \) for treatment of C. difficile occurs after the release of positive laboratory testing. Screening of in-hospital patients is considered for those with potential exposure to CDI through colonized patients, staff, or contaminated environment and equipment. In this model, we assumed that the same laboratory testing method was used for screening of patients at the time of admission and in-hospital patients.

The effects of treatment, screening, and the development of immune responses upon colonization are included in the reduction of disease transmission and transitions between different model compartments. Considering a mass-action incidence for disease transmission with homogenous mixing, the model can be expressed by systems of differential equations (see Additional file 1).

The basic reproduction number, commonly denoted by R ₀, is defined as the average number of secondary cases generated by an infectious case introduced into an entirely susceptible population [33]. We applied the next generation method [33] to calculate the reproduction number in terms of the model parameters. Using this method in the absence of treatment or screening (see Additional file 1), we obtain the basic reproduction number in terms of the model parameters:

The description of the parameters in the expression for R ₀ is provided in Table 1. In this expression, β represents the baseline transmission rate for patients with CDI symptoms. Given a reproduction number, the transmission rate in simulated scenarios was calculated from the above expression while fixing other parameters.

We implemented the model stochastically, and used the Gillespie direct algorithm to simulate the stochastic model within a (non-ICU) hospital ward with 50 beds (as the population size) within the range of previous studies for C. difficile [18]. To estimate the transition time between the two consecutive events in the stochastic process, we let dt =  − log(n ₁)/Δ, where n ₁ is a random number drawn from the uniform distribution on the unit interval [0, 1], and Δ is equal to the sum of the rates for all possible events. We then ordered the events as an increasing fraction of Δ and generated another uniform number n ₂ between 0 and 1 to determine the nature of the next event. We ran 500 independent simulations to calculate the average of sample realizations of the stochastic process in each scenario.

To simulate the stochastic model, we extracted a number of parameter values from the previous literature. The mean values of these parameters were used for the main results, and the estimated ranges were explored in the sensitivity analyses to investigate the relative influence of each parameter on CDI prevalence. We varied R ₀ in the estimated ranges reported in two previous studies [14, 34]. Lanzas et al. [14] fitted a mathematical model to hospital data for patients between January and December 2008, during which C. difficile diagnosis was conducted by stool toxin, and estimated the mean reproduction number of 1.07 (range: 0.55–1.99). By linking the secondary cases to index cases using PCR ribotyping, Norén et al. [34] estimated the mean reproduction number of 2.6 (range: 1–7) for a single hospital ward data between February 1999 and January 2000. The transmission parameter was calculated based on a given R ₀, while fixing other parameters of the model. The rate of disease transmission by asymptomatic carriers or colonized patients who mount immune responses may be lower than those with CDI symptoms. While quantification for this lower transmission rate is lacking, we assumed a relative transmissibility that is reduced by 50% on average and considered a range of 30%–70% in the sensitivity analyses. The fraction of colonized patients who mount immune responses was set to 0.6 within the estimated range 0.45–0.75 [14, 15]. We considered a mean period of 5 days for colonized patients to develop symptoms [14, 15]. The duration of CDI symptoms was assumed to have a mean of 4 days [35], with an average of 5 days for full recovery after the resolution of symptoms [14, 15]. Treatment is assumed to be successful in 80% of CDI patients [14, 15]. Based on reported cases [20], we assumed 4.8% of the screened patients admitted to the hospital were colonized [28], and therefore 95.2% were assumed to be susceptible. We used the rate of 6.9 per 10,000 patient-days estimated over 82 periods of 4 weeks each to calculate the daily fraction 1.22 × 10⁻⁴ of patients admitted to the hospital presenting CDI symptoms [20]. We assumed 22% of screened patients who are susceptible to colonization receive antibiotic treatment [14]. The rate of in-hospital antibiotic treatment damaging gut flora was set to 0.11 per day [36], and the rate of recovery was assumed to be 0.011 per day [37]. The risk of antibiotic-associated C. difficile colonization relative to no antibiotic exposure has been reported to vary in a wide range of 1.8–16.8 [24, 38]. We considered a 5-fold higher risk of C. difficile colonization for patients under antibiotic treatment. The discharge rate (including mortality) is assumed to be 0.17 per day for hospital patients without CDI symptoms, with a CDI-induced mortality rate of 0.0012 per day for patients with C. difficile symptoms [14, 15]. The discharge rate corresponds to an average of 5.9 days for the length of hospital stay. For scenario evaluation, the fraction of patients screened at the time of admission was set to 0.925 [20]. This fraction for screening in-hospital patients with potential exposure to CDI was assumed to be 0.9. The effectiveness of patient isolation, represented by the parameter ξ in the model, was varied in the range 0.8–1. To account for the effect of imperfect isolation, we multiplied the factor (1 − ξ) by the baseline transmission (β) in the model equations (See Additional file 1). Parameter values and their respective ranges are provided in Table 1.

For the mean value of R ₀ = 1.07 in the range 0.55–1.99 [14], Fig. 2 shows the prevalence of C. difficile for three scenarios in which the effectiveness of patient isolation in preventing infection transmission is 100% (Fig. 2a, d), 90% (Fig. 2b, e), and 80% (Fig. 2c, f). In these simulations, the baseline scenario without screening (θ = 0) was compared with the scenario of 92.5% screening at the time of hospital admission. When the effectiveness of patient isolation is 100%, the prevalence of C. difficile (i.e., the sum of black and grey curves) is reduced from 5.7 cases without screening to 2.1 cases (on average) with 92.5% screening of patients at the time of admission. This corresponds to 63.2% reduction of prevalence 50 days after the start of screening. For imperfect isolation with less than 100% effectiveness, the benefits of screening and detection of colonized patients are reduced as a result of within-ward transmission. For example, an isolation measure with 90% effectiveness reduces the prevalence by 54.2% from an average of 7.2 cases without screening to 3.3 cases with screening. When the effectiveness of patient isolation is further reduced to 80%, the percentage reduction of the prevalence of C. difficile with screening is at 41%. Results for a higher reproduction number (R ₀ = 2.6) show that the reduction of the prevalence is substantially reduced for the corresponding scenarios (Additional file 1: Figure S3).

Figure 3 shows the prevalence of C. difficile when an average of 2 days is considered for time delay between sample collection and the release of laboratory results. Compared to the results for rapid testing, we observed significantly lower effect of screening on reducing the prevalence of CDI. When the effectiveness of patient isolation is 100%, the prevalence of C. difficile reduces from 5.7 cases (on average) without screening to 5.3 cases (on average) with 92.5% screening of patients at the time of hospital admission. This corresponds to only 7% reduction of prevalence 50 days after the start of screening. For an isolation strategy with 90% or 80% effectiveness, the percentage reduction of the prevalence of C. difficile with screening remains below 6%.

Our simulations show that, for a sufficiently high transmissibility of CDI, the disease persists within a hospital setting in the presence of in-ward transmission, even when there are no asymptomatically colonized patients at the time of hospital admission. Figure 4 shows the persistence of CDI for R ₀ = 1.8 (grey curves) and R ₀ = 2.6, (black curves) when hospital admission occurs only through susceptible compartments in the model (i.e., b _s  = 1). This suggests that the admission of asymptomatically colonized patients is not the sole factor in persistence of CDI in hospital settings.

We also evaluated the percentage reduction achieved in the number of new infections (i.e., the incidence) over the period of 200 days. Figure 5a (black curve) shows that when the effectiveness of patient isolation is 100% in preventing infection transmission in the model with rapid testing, the daily incidence of C. difficile is reduced by over 79% [95% CI: 78% – 79.6%] as a result of 92.5% screening at the time of hospital admission. With lower effectiveness of isolation, this reduction is decreased (Fig. 5a, red and grey curves) to 62.6% [95% CI: 61.8% – 63.4%] (and 44.2% [95% CI: 43.5% – 44.9%]) for patient isolation with effectiveness of 90% (and 80%).

For the model with an average time-delay of 2 days between sample collection and the release of laboratory results, the relative reduction of incidence is significantly lower at 16.3% [95% CI: 15.1% – 17.4%], 10.2% [95% CI: 9.0% – 11.5%], and 10.1% [95% CI: 9.4% – 11.2%] when the effectiveness of patient isolation is 100%, 90%, and 80%, respectively (Fig. 5c).

For the scenarios in which patient isolation was less than 100% effective in preventing in-ward transmission, we implemented screening of inpatients with exposure to C. difficile in addition to screening of patients at the time of admission (Fig. 5b, d). For the model with rapid diagnostic testing, Fig. 5b shows the percentage reduction of the incidence of C. difficile, when screening 90% of in-hospital patients started on day 100. This resulted in an increasing trend in the percentage reduction of C. difficile incidence over time, reaching levels over 76% and comparable to those achieved with screening patients only at the time of hospital admission when the effectiveness of patient isolation is assumed to be 100% (Fig. 5a, black curve). However, simulating the model with a 2-day delay in release of laboratory results indicates little additional benefits, achieving only 6% increase in the relative reduction of CDI incidence by inpatient screening (Fig. 5d). When the effectiveness of patient isolation is lower at 80%, the effect of inpatient isolation becomes more pronounced (Fig. 5b, grey curve) in the model with rapid testing.

Similar results were obtained for the prevalence of CDI. Additional file 1: Figure S2 shows that, in the model with rapid testing, the prevalence of CDI reduces and stabilizes at a lower level compared to the level achieved prior to 100 days with screening patients only at the time of hospital admission (Additional file 1: Figure S2A,B). However, for the model with time delay in laboratory testing, we observed virtually no change in the prevalence of CDI after implementing inpatients screening (Additional file 1: Figure S2C,D).

Our analysis (detailed in Additional file 1) reveals that for a low reproduction number (R ₀ = 1.07), the fraction of admitted patients who are susceptible to colonization (b _s ; PRCC > 0.80, p-value < 0.001) and the fraction of patients who are screened at the time of hospital admission (θ; PRCC > 0.7, p-value < 0.001) have the highest impact on the CDI prevalence based on their PRCC values; both of which are negatively correlated with the response (Additional file 1: Table S1). However, for a higher reproduction number (R ₀ = 2.6), the risk of acquiring infection as a result of exposure to antibiotics (ψ; PRCC > 0.85, p-value < 0.001) was the parameter with the largest impact (Additional file 1: Table S2). The effect of immune responses on reducing disease transmission (υ; PRCC < − 0.87, p-value < 0.001) has a strong effect and negatively correlated with the response in all scenarios. With rapid laboratory testing, parameters with moderate effects on the response include the effectiveness of patient isolation and the probability of successful CDI treatment. When laboratory testing was associated with a time-delay, additional parameters with moderate effects include the relative transmissibility of asymptomatic carriers and the relative risk of colonization with antibiotic exposure. Furthermore, the time-interval between sample collection and the release of laboratory results had a low to moderate effect on the response. The relative influence of model parameters with R ₀ = 1.07 is summarized in Table 2. These results suggest that several factors contribute to the ‘silent transmission’ of C. difficile through asymptomatic carriers, which is the main driver of infection spread in the hospital [39].