2.4.1. Patients.

Upon admission, a patient can be either Susceptible (S) or Infectious (I). During hospitalization, a Susceptible patient can become Exposed (E) after exposure to a reused contaminated material. We denote as the status (i.e., 0 for S, 1 for E, or 2 for I) of patient s at time t. Initial statuses of patients are randomly drawn according to a vector of upon-admission prevalences giving the initial prevalence (i.e., probability of being pathogen-positive when entering the hospital) for each group of patients.

A device of type k is reused on patient s at time t for procedure p in ward w if no new device is available in the ward (i.e., ). The contamination status of the device is defined by , which follows a Bernoulli law with (contaminated device) and (uncontaminated device).

The time-dependent probability of a susceptible patient getting infected after exposure to reused contaminated devices during procedure p in ward w is computed as:

Where is the vector of device types used during procedure p, and is the risk of infection after exposure to a contaminated device during the same procedure, randomly drawn in an associated risk distribution.

If infection occurs, the patient becomes exposed, and his status changes to . The patient stays in the exposed state until the end of an eclipse phase e is reached. This corresponds to the pre-ramp-up phase of the pathogen’s natural history, during which the patient’s infectiousness is considered null. The eclipse phase duration is drawn in a uniform distribution with parameters and for each new patient s entering the hospital:

A counter of the number of time-steps since exposure is initialized upon admission and is given at each time-step by:

If , the eclipse phase is over, and the exposed patient becomes infectious () until he leaves the hospital.

2.4.2. Devices.

At each time step, in each ward, patients undergo their procedures successively. When patients in ward w need to undergo a procedure requiring a device of type k, these procedures requiring the same device type are performed randomly. The rank of patient s is then denoted among all procedures requiring device k at time t in ward w.

Any device not already contaminated and used on an infected individual is considered contaminated after exposure. However, after each procedure, the device undergoes a sterilization process, which successfully clears contamination with probability .

To that aim, we define as a device-dependent random variable following a Bernoulli distribution (i.e., the device is well disinfected or insufficiently disinfected) with = and = .

Between times t and t +1, the dynamics of device type k in ward w are thus described by the following systems of equation:

If :

If :

Where is the increment of time step generated by a procedure using device k performed on patient s and is the total number of patients undergoing a procedure requiring device k in ward w at time t.

Finally, each type of device undergoes a full renewal at a given device-dependent and ward-dependent frequency . New devices then replace all previously used devices of that type.

2.6.1. Application to HCV in an Egyptian hospital: baseline scenarios.

We used detailed longitudinal data collected in an Egyptian hospital (Ain-Shams University Hospital, Cairo) in 2017 over six months to inform multiple parameters of our model. Five hundred patients were screened upon admission for HCV positivity and followed throughout their hospitalization in the Surgery and Internal Medicine departments. Many data were collected: (a) Upon-admission patient characteristics such as age, gender, and history of previous hospitalization, (b) patient location within the hospital, and (c) procedures undergone by these same patients. More details on the collected data are available in Anwar et al., 2021 [7].

These data were used to parametrize the model in the particular estimate: (a) The initial prevalence, (b) the number of patients, (c) the number of wards, (d) the number of procedures, (e) the transition matrix between wards within the hospital, and (f) the probability matrix associated with the procedures. These parameters were estimated separately for both departments (i.e., patient profiles). As the minimum duration of a procedure in our data was 5 minutes, we considered a 5-minute time-step for our transition matrix and procedures probability matrix estimations. In addition, we used other data collected for the year 2015 to inform the quantity of available supply within this same hospital, the date of resupply, as well as the admission probability in each department. The values of all these parameters and the method used to estimate the resupply date are detailed in the supplementary material (S3–S10 Tables and S1–S3 Figs and S1 Text).

Finally, per-procedure transmission risks were retrieved from a previously published risk-assessment [8], and the minimum and maximum durations of the eclipse phase were found in the literature [9]. No information was available to estimate the probability of successful sterilization for each device, so these were informed based on the expert opinion of our Egyptian collaborators (AAS, WA,SA). As Ain-Shams is a University Hospital where adherence to control measures is usually high, the probability of successful sterilization was set to 95% for all device types.

In addition to the baseline scenario exploring transmission within a high-resource setting, we explored the case of a hospital with lower resources and lower adherence to control measures. To that aim, we divided the quantity of available supply by two, and the resupply frequency was estimated with this new information. In addition, the probability of successful sterilization was reduced to 80% for all device types.

Our model was run over a year, representing 105,120 time steps. The main outcomes retrieved from our simulations were the daily HCV incidence rate as well as the yearly cumulative incidence at a hospital and ward level. In addition, we estimated the yearly portion of new HCV cases attributable to each type of device.

2.6.2. Interventions: reinforced infection control.

We then simulated two different interventions based on HCV testing to reduce the risk of infection for hospitalized patients:

1. A targeted ward-level systematic-screening intervention. The three most at-risk wards (i.e., with the highest yearly estimated cumulative incidence) were identified after running baseline scenarios. Every patient entering one of these wards was assumed to be screened for HCV. Reinforced infection control was then implemented for identified positive patients, simulated as systematic successful sterilization of devices following use on these patients (i.e., the probability of successful sterilization was set to 1).
2. A random screening upon admission intervention. A random subset of patients entering the hospital were assumed to be screened for HCV. Reinforced infection control was then implemented for identified positive patients, simulated as systematic successful sterilization of devices following use on these patients.

The total number of tests performed in the three wards targeted by the systematic-screening intervention over a year was retrieved so that the number of random tests in the random screening upon admission intervention was set to be the same in order to compare these two scenarios. Test sensitivity and specificity were both assumed to be 100%.

2.6.3. Sensitivity analysis.

Various sources of uncertainty might have interfered with the per-procedure risk estimations. In particular, the risk associated with surgery was estimated based on ORs reported in multiple studies. However, no information was available on whether this procedure described the procedure itself or took into account surgeries and other often associated sub-procedures (such as intubation or injection, for example) as a whole. Thus, a sensitivity analysis was performed in order to compare our baseline assumption (this risk is, in fact, associated with the act of surgery itself) with the case, considering that this risk already takes into account the risk of other associated sub-procedures, and then deleting in our data all procedures occurring in the operating room except the ones reported as surgeries.

2.6.3. Extension to HBV.

To illustrate how the model may also be used to study HBV transmission in hospitals, we applied it to the case of an Ethiopian hospital, in which high levels of HBV prevalence were found recently. We assumed a similar hospital structure with three modified input parameters:

1. The initial prevalence. We retrieved age-specific HBV seroprevalence from Mohammed et al. (2022) [10], who explored HBV infections in two Ethiopian hospitals.
2. The per-procedure infection risks. We estimated per-procedure infection risk distributions for HBV by multiplying those computed for HCV by the ratio of the probability of HBV infection after exposure to contaminated blood (6–30%) over the same probability for HCV (1.8%) [11].
3. The duration of the eclipse phase. Its value for HBV was retrieved from the literature and estimated to be 15 days [12]

More information on these calculations is available as Supplementary Material. All other parameters were kept unchanged. We explored the same scenarios for HCV (high-resource vs. low-resource hospitals) and assessed the same interventions (systematic- vs. random screening).

2.6.6. Model simulations.

This model was coded in C++ using the Rcpp interface in R version 4.3.1 [13,14]. All simulations were performed using the same R version. The number of simulations needed to catch most of the variability produced by the model was estimated by studying the convergence of the cumulative mean of the number of yearly cases for the low-resource setting scenario. S8 Fig shows that the mean converges after approximately 100 simulations. Therefore, each scenario was simulated 100 times. All simulations were distributed across 18 CPU threads (running at 4.8Ghz with 64Gb of RAM) using the R packages ‘parallel’ [14] and ‘doParallel’ [15]. The average computation time for 100 simulations of a scenario was 25 minutes.

3.1.1. Baseline scenarios.

The predicted yearly number of HCV acquisitions among hospitalized patients differed highly depending on the scenario.

In the high-resource setting case, this number was estimated to be around 1.1 cases per 100,000 patients/year (95% PI [0–4.0]) (Fig 2A). The yearly incidence rate was the highest in the OR (3.94 cases per 100,000 per year, 95% PI [0–17.0]), ER ICU (1.6 cases per 100,000 per year, 95% PI [0–1.6]), and ER (0.08 cases per 100,000 per year, 95% PI [0–1.6]) wards (Fig 2B), though accounting for 0.72, 0.08 and 0.04 annual cases on average, respectively. The type of device associated with the largest number of HCV contaminations was the endotracheal tube, with 90% of all cases on average (Fig 3A).

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Fig 2. Results of the model for baseline scenarios (HCV case).

(A) and (C): Daily incidence rate for the high- and low-resource hospitals, respectively. (B) and (D) Yearly cumulative incidence (mean and 95% PI) and average number of cases for each ward, ranked by mean cumulative incidence values.

https://doi.org/10.1371/journal.pcbi.1012850.g002

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Fig 3. Yearly attributable portion to new cases for each device, in (A) Baseline scenario for the high-resource and (B) Baseline scenario for the low-resource hospital.

https://doi.org/10.1371/journal.pcbi.1012850.g003

In the low-resource setting, the average yearly number of cases was estimated at around 60 per 100,000 patients/year (95% PI [46.25–87.01]) (Fig 2C). The ER ICU, OR, and ER wards were associated with the highest yearly incidence, with 196.7 cases per 100,000 patients/year (95% PI [0–521.72]), 64 cases per 100,000 patients/year (95% PI [19.9–109.6]) and 29.6 cases per 100,000 patients/year (95% PI [18.8–49.3]) respectively (Fig 2D). IV cannulas were associated with the highest number of HCV contaminations, representing around 22% of all HCV infections on average, followed by lancets (around 18% of all infection cases) (Fig 3B).

3.1.2. Interventions.

In each case (i.e., high-resource or low-resource setting), the efficacy of the targeted ward-level systematic screening interventions was superior to that of the upon-admission random-testing interventions (Fig 4).

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Fig 4. Reduction in the predicted yearly cumulative incidence, by comparison with the baseline scenarios, obtained by two different intervention strategies implemented in (A) high-resource and (B) low-resource hospitals.

Baseline scenarios correspond to the no-intervention scenarios. For both high-resource and low-resource settings, on average, 53,640 patients (72%) were screened (i) either systematically (in the three most at-risk wards) or (ii) randomly upon admission. Median relative reductions computed over 100 simulations, along with the first and third quantiles (boxes) of the associated distributions and the 95% prediction intervals, are depicted.

https://doi.org/10.1371/journal.pcbi.1012850.g004

For both the high and low-resource setting cases, the OR, ER ICU, and ER wards were the most at-risk ones. A total average number of 53,640 patients (72%) went through these three wards during their hospitalization.

For the high-resource setting case, performing systematic screening in these three most at-risk wards reduced the annual number of HCV acquisition cases by 100% on average (95% PI [100–100]) compared to the baseline scenario, whereas random testing in 72% of patients upon admission reduced the annual number of cases by 81.3% (95% PI 0–100]).

Trends were similar for the low-resource setting case. Performing systematic screening in the three most at-risk wards allowed a reduction of 83.3% (95% PI [72.4–92.9]). Performing random screening in 72% of newly admitted patients reduced the annual number of cases by 73.2% (95% PI [57.1–85.1]).

3.1.3. Sensitivity analysis.

When considering that our estimate of HCV infection risk associated with surgery already takes into account the risk of other associated sub-procedures, the yearly cumulative incidence was reduced by 85.6% in the high-resource setting baseline scenario (with 0.16 cases per 100,000 patients/year; 95% PI [0–1.88]) and there was no change in the low-resource setting baseline scenario (60.3 cases per 100,000 patient/year; 95% PI [42.6–85.4]), compared to the baseline case where each of the procedures occurring in the operating room was taken into account individually.

3.2.1. Baseline scenarios.

The predicted number of HBV acquisitions among hospitalized patients again differed highly between low- and high-resource hospital settings (S5 Fig).

In high-resource settings, this number was estimated at 12.6 cases per 100,000 patients/year (95% PI [5.5–20.3]), with the OR ward being the most at-risk, with a yearly cumulative incidence of 55.6 cases per 100,000 patients/year (95% PI [18.3–92.4]), followed by the ER ICU ward (7.7 cases per 100,000 patient/year, 95% PI [0–77.7]) and the Neurosurgery ward (3.4 cases per 100,000 patient/year, 95% PI [0–42.3]). The type of device associated with the highest number of HCV contaminations was the endotracheal tube, with more than 85% of all cases on average (S6 Fig).

For low-resource settings, the yearly cumulative incidence reached 677.5 cases per 100,000 patient/year (95% PI [584.5–749.6]), with the ER ICU ward again being one of the most at-risk with a yearly cumulative incidence of 2,243.7 cases per 100,000 patient/year (95% PI [1,002.3–3,237.43]), followed by the OR ward (686.4 cases per 100,000 patient/year, 95% PI [530.1–850.8]), and the ER ward (344.4 cases per 100,000 patient/year, 95% PI [285.2–409.0]). IV cannulas were associated with the highest number of contaminations, accounting for around 22% of all contaminations, on average (S6 Fig).

3.2.2. Interventions.

The same trends as for the HCV case were observed in the HBV case (S7 Fig). Systematic screening in the most at-risk wards (representing 72% of all patients) was found to reduce the number of cases by 97.1% (95% PI [83.0–99.3]) in the high-resource hospital. On the other hand, the reduction was 71.3% on average (95% PI [37.5–98.0]) when randomly screening patients upon admission.

For the low-resource hospital, the reductions obtained by these same interventions targeting 72% of patients were 81.5% (95% PI [77.2–85.1]) and 71.1% (95% PI [64.4–78.3]), for the systematic and random screening interventions, respectively.