Modeling fomite‐mediated SARS‐CoV‐2 exposure through personal protective equipment doffing in a hospital environment

Abstract Self‐contamination during doffing of personal protective equipment (PPE) is a concern for healthcare workers (HCW) following SARS‐CoV‐2‐positive patient care. Staff may subconsciously become contaminated through improper glove removal; so, quantifying this exposure is critical for safe working procedures. HCW surface contact sequences on a respiratory ward were modeled using a discrete‐time Markov chain for: IV‐drip care, blood pressure monitoring, and doctors’ rounds. Accretion of viral RNA on gloves during care was modeled using a stochastic recurrence relation. In the simulation, the HCW then doffed PPE and contaminated themselves in a fraction of cases based on increasing caseload. A parametric study was conducted to analyze the effect of: (1a) increasing patient numbers on the ward, (1b) the proportion of COVID‐19 cases, (2) the length of a shift, and (3) the probability of touching contaminated PPE. The driving factors for the exposure were surface contamination and the number of surface contacts. The results simulate generally low viral exposures in most of the scenarios considered including on 100% COVID‐19 positive wards, although this is where the highest self‐inoculated dose is likely to occur with median 0.0305 viruses (95% CI =0–0.6 viruses). Dose correlates highly with surface contamination showing that this can be a determining factor for the exposure. The infection risk resulting from the exposure is challenging to estimate, as it will be influenced by the factors such as virus variant and vaccination rates.


| INTRODUC TI ON
Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is an enveloped virus which has infected in excess of 200 million people to date and caused more than four million deaths worldwide according to Johns Hopkins University's COVID-19 dashboard. 1 Inanimate objects known as fomites may host pathogens and have the potential to contribute to transmission in healthcare environments. This occurs in viral contamination spread [2][3][4] including SARS-CoV-2. 5,6 However, it should be noted that there are uncertainties as to the relationship between the molecularly detected viruses and infectious viruses. In terms of persistence, there appears to be a similarity between SARS-CoV-1 and 2 on surfaces, where initial concentrations of 10 3.7 median tissue culture infectious dose (TCID 50 )/ml (SARS-CoV-2) and of 10 3.4 TCID 50 /ml (SARS-1) reduced to 10 0.6 TCID 50 /ml (SARS-CoV-2) and 10 0 . 7 TCID 50 /ml (SARS-1), respectively, due to the decay of viability of the virus after 72 h on plastic surfaces. 7 Persistence on the scale of days under heavy contamination conditions allows an opportunity for exposure through hand-to-fomite contacts. Although personal protective equipment (PPE) such as gloves, gowns, and masks are worn to protect both patients and healthcare workers (HCW) from the exposure, self-contamination during PPE doffing processes 8,9 poses risks to HCW and enables spread from one patient to another during multiple care episodes. SARS-CoV-2 has been detected on healthcare worker PPE 10  While SARS-CoV-2 has been detected on PPE and patient surfaces, the relationship between viral RNA concentrations and risk of infection is still unknown. 11 Bullard et al. 12 present TCID 50 and cycle threshold values relative to days since symptom onset, but these may not be translatable to concentrations on fomites due to the potential for more SARS-CoV-2-genetic material corresponding to inactivated viruses resulting from incomplete surface disinfection practices. Quantitative microbial risk assessments (QMRA) involve the use of mathematical models to estimate doses of a pathogen and subsequent infection risk probabilities. Quantifying infection exposure and risk for any given dose can be used to guide intervention decision-making and have been used in other public health contexts, such as in setting water quality standards. 13 These typically rely on experimental doses of a microorganism inoculated into healthy participants or mice models in a known quantity. Whether they develop the infection can then be recorded. 13 QMRA modeling and surface contact models have been used to evaluate multiple transmission pathways. The role of care-specific behaviors in environmental microbial spread 14 includes the effect of glove use in bacterial spread from one surface to another 15 and evaluating risk reductions through hand hygiene or surface disinfection interventions. [16][17][18] While a strength of QMRA is related to environmental monitoring data to health outcomes, a common limitation is the lack of specific human behavior data such as hand-to-face or hand-tosurface contact sequences that result in dose exposures. 18,19 The use of the QMRA modeling framework incorporating care type surface contact patterns before potential self-contamination via PPE doffing will offer insight into viral exposure per shift.
The objective of this study is to relate SARS-CoV-2 concentrations on surfaces to predict the exposure of a single healthcare worker over an 8-hour shift and estimate the effects of doffing mistakes and number of care episodes per shift on inoculated dose per shift.

| ME THODOLOGY
This approach combines human behavior and fomite-mediated exposure models of 19 hospital scenarios, for which concentrations of SARS-CoV-2 on hands and infection risk for a single shift are estimated for a registered nurse, an auxiliary nurse, and a doctor.
A control scenario was defined as a single episode of care with a SARS-CoV-2-positive individual with an assumed 80% probability of self-contamination during doffing: a "worst-case scenario." Eighteen other scenarios covered three likelihoods of self-contamination: 10%, 50%, and 80%, ×2 caseload conditions: 7 patients (low) vs. 14 patients (high) × 3 probabilities of any given patient being COVID-19 positive: low (5%), medium (50%), and a 100% COVID-19-positive ward. These rates of self-contamination during doffing were assumed due to uncertainty as to how workload and stress, especially under pandemic conditions, would influence doffing. Exploring probabilities of self-contamination as low as 5% and as high as 80% allows for the exploration of optimistic and worse-case scenarios.
During low caseload conditions, it was assumed that the number of care episodes per shift would be less 7 than that of the high load conditions. 14 The assumed number of patient care episodes when PPE is worn per shift for low and high caseload scenarios were 7 and 14, respectively, based on a respiratory ward in a university teaching hospital in the UK. The low caseload estimate was based on the communication with a UK NHS consultant, who tracked the number of gowns used by healthcare workers over a week on a mixed COVID-19 8-bed respiratory ward. All model parameters are described and reported in Table 1. Per scenario, three simulations were

Practical Implications
Infection risk from self-contamination during doffing PPE is an important concern in healthcare settings, especially on a COVID-19 ward. Fatigue during high workload shifts may result in an increased frequency of mistakes and hence the risk of exposure. Length of staff shift and a number of COVID-19 patients on a ward correlate positively with the risk to staff through self-contamination after doffing.
Cleaning of far-patient surfaces is equally important as cleaning traditional "high-touch surfaces," given that there is an additional risk from bioaerosol deposition outside the patient zone.
run where sequences of hand-surface contacts per care episode were care-specific (IV care, observational care, or doctors' rounds).   weighted probabilities. 14 More information regarding the observation of these behaviors and analysis of sequences of events can be seen in King et al. 20 The transition of an HCW between surface contacts is modeled using a discrete-time Markov chain approach. 14 Using defined weighted probabilities based on observation of patient care, surface contact by HCW can be simulated based on the property that given the present state, the future and past surfaces touched are independent. This is termed as the Markov property (Equation 1):

| Healthcare worker surface contact behavior sequences
where X n represents the surface contacted in the nth event, i and j are two surfaces, and P represents a conditional probability. This is then denoted as P j→i for the ease of notation. For example, the probability if the HCW is currently touching the table and they will next touch the chair is P table→chair and can be worked out by counting the number of times this happens during care divided by the number of times any surface is touched after the table. 21 Discrete-time Markov chains were fitted to observed care contact sequences using the "Markov chain Fit" function from the R package Markov chain (version 0.7.0). Separate Markov chains were fitted to IV care, doctors' rounds, and observational care sequences.
States included "in" (entrance to the patient room), "out" (exit from the patient room), contact with a far-patient surface, contact with a near-patient surface, contact with a hygiene surface (e.g., tap, sink, soap, or alcohol dispenser), and contact with equipment. For each episode of care, the first event was the entrance into the patient's room. It was assumed in the simulation that all HCWs wore a gown, gloves, mask, and face shield when entering the room in that handto-face contacts were not modeled during the episodes of care, and hand hygiene moments only occurred after doffing in between the care episodes. The episode of care ended when an "out" event occurred.

| Exposure model
Accretion of microorganism on hands from the surface contacts has been demonstrated 14 to respond to a recurrence relationship with the concentration on hands after the nth contact, C h n , with the concentration on hands, C h This is an adaptation of the pathogen accretion model (PAM) from King et al. 14 and a gradient transfer model by Julian et al. 22 Here, the concentration on hands for contact n is equal to the previous concentration on the hand (C h n−1 ) after adjusting for inactivation for the virus on the hand (k h ) and surface k s , minus the removal from the hand due to the hand-to-surface transfer plus the gain to the hand due to surface-to-hand transfer. Δt is the time taken for an episode of patient care and sampled from a uniform distribution of range 2-20 min. 23 Here, and represent hand-to-surface and surface-to-hand transfer efficiencies, respectively. The fraction of the total hand surface area (S h ) is used to estimate how much virus is available for transfer, given a concentration of the number of viral particles/cm 2 on the gloved hand and surface.

| Estimating inactivation on the hand
Sizun et al. evaluated the survival of human coronaviruses (HCoV) strains OC43 and 229E on latex glove material after drying. Within 6 h, there was a reduction in viral infectivity for HCoV-229E that we assume is equal to 99%. 24 For HCV-OC43, a reduction of approximately 99% in viral infectivity occurred within an hour. 24 Harbourt et al. 25 measured SARS CoV-2 inactivation on pig skin with virus remaining viable for up to 8 h at 37°C. We, therefore, used a uniform distribution with a minimum of 1 h and a maximum of 8 h to estimate a distribution of k h inactivation rates.

| Estimating inactivation on surfaces
The decay of the virus causing COVID-19 has been shown to vary under both humidity and temperature, but in contrast with the previous findings, 7 it appears that the surface material may not have a large impact on the decay rate. 25 We, therefore, use one distribution of inactivation rates regardless of surface type by taking a conservative approach and using an averaged half-life τ estimate for stainless steel-and plastic-coated surfaces at 21-23°C 7 at 40% relative humidity, which are 5.63 h (95%CI = 4.59-6.86 h) and 6.81 h (95%CI = 5.62-8.17 h), respectively. We assume a first-order decay (Equation 3) to estimate the inactivation constant k which we use here for brevity instead of k s and k h in the Equation (2).
Surface viral concentration C at any given time t then depends uniquely on initial concentration C 0 . Where the half-life τ, is related to k by: k s = log(2)∕ . Since the hospital rooms are made up of a combination of stainless steel and plastic surfaces, we have taken the widest confidence interval as bounds when sampling from a uniform distribution for inactivation rate k s . Inactivation on gloves is assumed to be minimal for the time scale of a care episode (2-20 min). 23

| Fractional surface area
For contacts with the door handle during "in" or "out" behaviors, a fractional surface area was randomly sampled from a uniform distribution with a minimum of 0.10 and a maximum of 0.17 for open hand grip hand-to-object contacts. 26 For contacts with the patient, a fractional surface area was randomly sampled from a uniform distribution with a minimum of 0.04 and a maximum of 0.25, for front partial finger or full front palm with finger contact configurations. 26 For contacts with other surfaces, the fractional surface areas were randomly sampled from a uniform distribution with a minimum of 0.008 and a maximum of 0.25, spanning multiple contact and grip types from a single fingertip up to a full palm contact. 26

| Transfer efficiencies
All transfer efficiencies used in this model are unitless fractions ranging from 0 to 1, representing the fraction of viruses available for transfer that transfer from one surface to another upon contact. For contacts with surfaces other than the patient, a truncated normal distribution with a mean of 0.123 and a standard deviation of 0.068 with maximum 1 and minimum 0 was randomly sampled for surfaceto-finger (λ) transfer efficiencies based on aggregated averages of influenza, rhinovirus, and norovirus. 4 For patient contacts, transfer efficiencies were randomly sampled from a normal distribution with a mean of 0.056 and a standard deviation of 0.032, left-and righttruncated at 0 and 1, respectively. The mean and standard deviation were informed by transfer efficiencies for rhinovirus measured for direct skin-to-skin contact. 27 Transfer efficiencies from fingers to surfaces (β) are assumed to be normally distributed with a mean of 0.118 and a standard deviation of 0.088. 4

| Surface concentrations
If the patient was assumed to be infected, surface contamination levels (RNA/swab surface area) were sampled from a triangular distribution where the minimum and maximum were informed by minimum and maximum contamination levels reported for the surfaces in an intensive care unit ward. 28 The median of these was used to inform the midpoint of the triangular distribution. 28  While a typical sampling size is 100 cm 2 , it may be as small as 10-25 cm 229-32 and in the real-world scenarios, sampling surface areas may be larger or smaller than these depending upon available surface area, ease of access, and the contamination magnitude expected.
Since the surface areas of these surfaces were not provided, a triangular distribution (min = 5, max = 195, mid = 100) describing the surface area (cm 2 ) of surfaces sampled was used to estimate RNA/cm 2 . Not all detected RNA was assumed to represent infectious viral particles. This is a conservative risk approach when utilizing molecular concentration data in QMRA. 33 Therefore, concentrations on surfaces C S (viable viral particles/cm 2 ) were estimated by Equation (4), where C RNA is the RNA/swabbed surface area, A surface is the surface area (cm 2 ) of the surface, and infective is the fraction of RNA that relates to infective viral particles (uniform(min = 0.001, max = 0.1)). This overlaps with a range used by Jones (2020) for COVID-19 modeling.
While data from Bullard et al. (2020) exist for relating molecularly detected SARS-CoV-2 to culturable SARS-CoV-2 for patient samples, these ratios do not translate to fomite scenarios where surface disinfection likely results in a more molecularly detectable viruses that do not translate to infectivity. Therefore, we did not use these data to inform our assumptions about viral infectivity for molecularly detected SARS-CoV-2 on surfaces.

| Estimating exposure dose
For all scenarios, it was assumed that the starting concentration on gloved hands for the first episode of care was equal to 0 viral particles/cm 2 . If gloves were doffed and a new pair was donned in between care episodes, it was assumed that the next episode of care began with a concentration of 0 viral particles/cm 2 on the gloved hands. After each care episode, a number was randomly sampled from a uniform distribution with a minimum of 0 and a maximum of 1. If this value was less than or equal to the set probability of selfcontamination during doffing, self-contamination occurred, where the fraction of total virus was transferred from the outer glove surface to the hands was assumed to be uniformly distributed between 3 × 10-5% and 10%. 8 There was then a 50/50 chance that either hand were washed or sanitized using alcohol gel due to the lack of available data describing proportions of hand hygiene attributable to these two methods occurring aftercare episodes. If they washed their hands, a log 10 reduction was randomly sampled from a normal distribution with a mean of 1.62 and a standard deviation of 0.12 (min = 0 and max = 6). 34 While these are not coronavirus-specific handwashing efficacies they allow for a conservative estimate. If hand sanitizer was used, a log 10 reduction was randomly sampled from a uniform distribution with a minimum of 2 and a maximum of 4. 35 To estimate a dose, an expected concentration on the hands after doffing and hand hygiene was estimated, followed by an expected transfer to a facial mucosal membrane during a single handto-nose contact after each patient care episode (Equation 5).
There was a 50/50 chance that either the right or left hand was used for this hand-to-face contact, as contact patterns between right and left hands have been shown to lack statistically significant differences. 36 Here, the transfer efficiency (T H→M ) of the hand-tonose contact was randomly sampled from a normal distribution with a mean of 33.90%, and a standard deviation of 13.18% based on a (4) 37 These simulated nose contacts were assumed to be with the mucosal membrane as opposed to other parts of the nose, such as the bridge of the nose, that would not result in a dose. The fractional surface area of contact (S m ) was assumed to be equal to one fingertip. To estimate this surface area, the minimum and maximum front partial fingertip fractional surface areas were divided by 5 to inform the minimum and maximum values of a uniform distribution. 24 The surface area of a hand (A h ) was randomly sampled from a uniform distribution with a minimum of 445 cm 2 and a maximum of 535 cm 2 19 and is informed by the values from the Environmental Protection Agency, USA's Exposure Factors Handbook. 38 The expected inactivation of the virus during this contact assumed a single second contact, and the final k h value used in the care episode simulation was used. Δt represents the time between the doffing and touching the mucosa. A total of 10 000 parameter combinations are obtained for each care type scenario in a Monte Carlo framework.

| Dose-response
Due to the lack of dose-response curve data for SARS-CoV-2, an exact beta-Poisson dose-response curve 39 was fitted to pooled data for SARS-CoV-1 and HCoV 229E, assuming the infectivity of SARS-CoV-2 lies between the infectivity for these two organisms.
In Equation (6) We use this dose-response curve within the discussion section as a comparator against the curve for HCoV229E also given in Ref. [39] which is considered a similar but more infectious virus.

| Sensitivity analysis
Spearman correlation coefficients were used to quantify monotonic relationships between input variables and viral exposure. This method has been used in other QMRA studies to evaluate the relationship between model inputs and outputs. 22

| Estimated dose
Dose values in Table 2 and Figure 3 are given in a number of virus plaque-forming units (PFU), where we also include all fractional values since these would correspond to multiple viruses for a higher surface load relating to different SARS CoV2 variants.
Median PFU values for each care type were within the same order of magnitude (see Table 2), while maximum values for IV drip were 47% higher than for observations and 68% than for Drs' rounds which can be explained by the number of surface contacts   Table 2. In terms of most important factors determining exposure, surface cleanliness was found to be the single most important, with hand-to-mouth/eyes/nose transfer efficiency only half as important (correlation coefficient ρ = 0.29 vs. ρ = 0.12, respectively) (see Table 3). Surface concentration relates to cleaning frequency; hence, the control case was run for half the surface bioburden.

| Key findings and generalizability
The model developed in this study indicates that the exposure from mistakes after doffing PPE is likely to be low for a single shift, even for nurses on 100% patient COVID-19 positive wards. Exposure doses vary by care type as greater frequencies of surface contacts directly impact viral loading on gloves and subsequent self- wards suggests aerosol deposition is a contributor to surface contamination, as one study has reported deposition at a distance of 3m from the patient. 11 Previous experimental work aerosolizing bacteria in an air-conditioned hospital room test chamber showed that surfaces well outside the patient zone can become contaminated with infectious material. 43,44 Since the observational study underlying the Markov chains reveals that at least 10% of staff contacts impact on such surfaces (excluding door handles), then the current lists of high-touch surfaces 45 that had historically been prioritized for cleaning, may need to be revised.
A dose-response curve for SARS-CoV-2 is not yet available; furthermore, the contribution of each dose (i.e., upper respiratory vs. lower respiratory route) to individual infection risk may still be unclear even if and when it is obtained. 46 Consequently, we have analyzed the results from the contact model based on relative exposures and qualitative trends to try and understand the effect of key parameters and mitigation strategies. In Figure 4, we plotted the risk [0-1] for each of the doses that the nurses received. We compare the prediction between the Beta Poisson dose-response curve presented above against that for HCoV229E. We also follow the approach from Lei et al. and assume that the dose required for infection from the upper respiratory tract relating to a mucosal contact is 100 times higher than a dose reaching the lower respiratory tract.
In general, the mean risk is higher than the upper quartile alluding to the hypothesis that a few nurses may become infected which relates to opportunistic or rare events under these circumstances.
Using a Bernoulli distribution with either a 1 or a 0 response, representing an infection or not from each one of the predicted exposure doses and corresponding individual infection risk probabilities, we can predict the number of nurses infected per 100 nurses. F I G U R E 2 Stair plot of example HCW surface contacts during care, where "patient" is a hand-to-patient contact; "out" and "in" are exit and entrance into the patient room, respectively; "FarPatient" is a hand-to-far patient surface contact; and "Equipment" is a hand-to-equipment surface contact  The spearman correlation coefficient represents instances in which these parameters were used in a simulation where a contaminated hand-to-face contact was made after doffing.

TA B L E 3 Spearman correlation coefficients of input parameters with infection risk
vaccine dose and 34 million, the second dose in the UK, which will substantially reduce the likelihood of infection further than those illustrated here.  Risk contamination. Future work should extend current models with a multi-exposure pathway approach. This will advance not only our understanding of SARS-CoV-2 transmission but the transmission of pathogens in built environments as a whole.

| Model uncertainties
It should be noted that there is still a large variation in gowns and masks and that there is the possibility of double gloving; hence, potentially reducing the risk of self-contamination and the type of material and the design will also to an extent, determine the contamination risk.
Finally, a dose-response curve informed by SARS-CoV-1 and HCoV-229E data was utilized, due to the lack of SARS-CoV-2specific dose-response data. Despite limitations related to the doseresponse, the conclusions from the estimated doses were consistent with the insights from infection risk estimates. Increases in the probability of contamination between care episodes related to increases in the dose and most notably, for scenarios in which more than 5% of patients had COVID-19 ( Figure 3).

| CON CLUS ION
We propose a model for predicting exposure to healthcare workers from self-contamination during the doffing of personal pro- if" parametric study and sensitivity analysis. Surface viral concentration was found to be more than twice as important as any other factor whereby highlighting the importance of time-appropriate cleaning. Transfer efficiency from finger to the nose was of secondary importance, although hand hygiene following doffing is still highly recommended. While the exposure from this type of selfcontamination is low per healthcare worker shift, this highlights that the procedures, if carried out correctly, are generally safe. It is accepted that other routes of transmission will play a significant role in infection propagation. Universal license (CC-BY), code can be accessed at: https://github. com/awils on12/surfa ce-conta m-model -COVID19.

CO N FLI C T S O F I NTE R E S T
None to declare.