MRSA transmission in hospitals across Alberta, Canada: a comparative study combining unidentified colonized cases upon admission

Abstract

Background

Methicillin-resistant Staphylococcus aureus (MRSA) is a prevalent bacterium in medical settings. It can result in bloodstream infections and other severe illnesses, and patients may have a high risk of dying from these conditions. This study aimed to examine MRSA transmission in hospitals across Alberta and how undetected colonized patients on admission affect MRSA spread.

Methods

We used a Bayesian compartmental model to simulate MRSA spread across 106 acute care hospitals in Alberta. The model assumes that MRSA spreads through interactions between susceptible individuals and MRSA patients, including both hospital-acquired (HA) and community-acquired (CA) MRSA cases. Data from Edmonton, Calgary, rural Alberta and all regions in Alberta were used to fit the model. We also assumed that a small percentage of patients were colonized upon admission but were not promptly identified in hospitals, and we tested the model assumptions. Transmission rates were estimated using a Bayesian framework with Markov chain Monte Carlo (MCMC) algorithms. We compared transmission rates across several regions in Alberta and assessed the effect of MRSA prevalence at hospital admission on MRSA transmission.

Results

When the model fit the data in hospitals in all areas of Alberta, the average number of susceptible people colonized due to patients with HA-MRSA colonization, patients with HA-MRSA infections, patients with CA-MRSA colonization, and patients with CA-MRSA infections per contact per month are around 0.03 (95% CI: (0.001, 0.101)), 0.08 (95% CI: (0.002, 0.278)), 0.01 (95% CI: (0.000, 0.033)) and 0.05 (95% CI: (0.001, 0.182)), respectively. Assuming 0.8 colonized cases per 1000 admissions, the average number of susceptible people who become colonized due to patients with HA-MRSA infections per contact per month in Edmonton, Calgary and rural hospitals are 0.05 (95% CI: (0.001, 0.174)), 0.43 (95% CI: (0.018, 1.152)) and 0.22 (95% CI: (0.007, 0.722)), respectively. Assuming more unidentified colonized cases in hospitals, transmission rates between susceptible people and infected patients increase marginally.

Conclusion

MRSA transmission rates appear to be marginally higher in Calgary hospitals compared to Edmonton, and rural hospitals seem to have lower transmission rates than in Calgary but higher than in Edmonton, with 95% credible intervals (CIs) overlapping. Our model also suggests that infected patients have a higher probability of transmitting MRSA to susceptible people in most Alberta hospitals.

Introduction

Staphylococcus aureus (S. aureus) is a widely distributed Gram-positive bacterium in human populations. Roughly 30% of individuals carry it constantly [1], while 60% of individuals carry it sporadically [2]. Many infections, including those in the bloodstream and lungs, are secondary to S. aureus. However, the overuse of methicillin-like beta-lactam antimicrobials has led to the emergence of methicillin-resistant S. aureus (MRSA). MRSA has caused significant morbidity and mortality in recent years. For example, MRSA was responsible for around 130,000 deaths worldwide in 2021 [3]. In 2022, MRSA accounted for around 21% of antimicrobial-resistant bloodstream infections in Canada [4]. Between 2018 and 2022, the death rate in Canada for MRSA bloodstream infections ranged from 16.3% to 19.8% [5].

People in acute care facilities are susceptible to MRSA colonization through direct skin contact with colonized or infected patients, particularly those with open wounds or compromised immune systems. Colonization may also occur via contact with contaminated healthcare workers (HCWs) or medical equipment [6]. Furthermore, a small proportion of people are already colonized or infected at the time of admission, with reported prevalence ranging from 0.25 to 2 cases per 1000 admissions [7]. Meanwhile, colonized patients in acute care hospitals are susceptible to infection [8]. Infections are more common in patients who have comorbidities and chronic disorders. Invasive treatments like indwelling urinary catheters can also be associated with infections since MRSA will quickly colonize and adhere to a catheter surface once it is implanted. Therefore, MRSA is considered a serious nosocomial bacterium, and extended hospitalization increases the risk of exposure to MRSA [9]. Hospital-acquired MRSA (HA-MRSA) cases refer to patients who become colonized or infected with MRSA while in the hospital.

MRSA has also grown increasingly prevalent in people who are not hospitalized. These individuals typically have not been admitted to any hospitals in the last year, so they are characterized as cases of community-acquired MRSA (CA-MRSA) colonization or infections. Hospitalization may be necessary for patients with CA-MRSA found in the community, resulting in potential transmission to more hospitalized patients [10].

Deterministic or stochastic compartmental models have often been used to examine the dynamics of MRSA spread in hospitals. Both kinds of mathematical models divide populations into distinct compartments, and each compartment symbolizes a particular group of people. They could be colonized or infected patients or others, such as healthcare professionals, and people in each compartment are usually assumed to be homogeneous [11]. The order of compartments demonstrates how MRSA transmits among distinct groups of people [12]. The deterministic approach typically uses ordinary differential equations to simulate an outbreak. In contrast, stochastic models take into account the uncertainties in an epidemic by using probability distributions. The uncertainties could be attributed to environmental or hereditary factors. MRSA latent durations or infectious periods are also frequently defined using stochastic models [11].

We can employ compartmental models to study the spread of MRSA, based on patient data, to better understand and predict transmission dynamics. The data typically record the number of positive cases in a certain time period in hospitals, but information regarding some characteristics that could affect transmission may not be recorded completely. Such latent information could include colonized patients upon admission, the rate of contaminated healthcare professionals among all hospital staff, and those who become colonized due to MRSA in the environment such as contaminated medical equipment [13]. When the data are linked to additional sources to increase their information, it can make models more adaptable [14]. For instance, Wang and Ruan [13] utilized hospital data to study the rate of environmental contamination caused by contaminated HCWs or MRSA patients. Their study assumed that MRSA spreads through contact from colonized patients to susceptible people. HCWs may contaminate MRSA and then contribute to the transmission. MRSA in healthcare settings may also affect its spread. In their model, certain parameters were approximated using both a deterministic and a stochastic formulation, whereas the values of other factors, such as the colonization rate upon admission, were derived from earlier studies [15, 16]. Similarly, Lee et al. [12] predicted the MRSA dissemination rate using stochastic models based on healthcare surveillance data. The model included susceptible individuals, as well as identified undiagnosed MRSA patients. When the model was fitted to the data, additional information such as the rate of colonization upon admission and discharges were based on previous research [17, 18].

Here, we employ a stochastic model to illustrate how MRSA disseminates in Alberta hospitals. Data used in the study come from hospitals across all areas of Alberta, and then are stratified into three additional groups: hospitals in Edmonton, Calgary, and rural areas including central, south and north areas of Alberta. To compare MRSA transmission across regions, we analyze each dataset separately and fit the model to each in a Bayesian framework. In some months, the number of MRSA colonizations in Calgary and rural Alberta hospitals is lower than the number of new infected individuals. The reason could be that certain individuals admitted to hospitals have been colonized [15], but these colonized patients are not included in our model or represented in the data. Therefore, our analyses assume a proportion of unidentified (or hidden) colonized patients upon admission to the model. We also consider a sensitivity analysis in which this proportion of undiagnosed colonizations is varied. By employing a model that attempts to capture the principles of transmission dynamics and making assumptions about unidentified colonized patients upon admission, we can compare MRSA transmission in different regions in Alberta.

Section 2 introduces the data used on MRSA in Alberta hospitals. The four datasets include data from hospitals in all areas in Alberta combined, then Edmonton, Calgary, and rural locations separately. Section 3 explains the peculiarities of MRSA transmission. We present the parameter set and likelihood function of the model. We also describe the Bayesian MCMC framework and demonstrate the assumptions of unidentified colonized patients upon admission. The results of the analysis in different regions of Alberta are shown in Sect. 4, along with the shift in transmission rates as the prevalence rate of colonized cases upon admission rises. Section 5 is the discussion of the study.

Data

Data consisting of the number of monthly MRSA colonized and infected cases in Alberta acute care hospitals are utilized in this study. The dataset originates from a provincial surveillance data management system used by the Infection Prevention and Control (IPC) program of Alberta Health Services (AHS) and Covenant Health [19]. At each hospital under the management of AHS and Covenant Health, the IPC surveillance program conducts surveillance for antimicrobial-resistant organisms. More than 4.5 million individuals in Alberta get acute care services from 106 acute care hospitals [20].

We concentrate on patients admitted to acute care facilities in Alberta from September 2018 to September 2023. Incident cases of MRSA, those identified with MRSA for the first time in hospitals, are included and classified as either colonization or infection. Cases of MRSA are divided into three classes based on their previous hospitalization and the time of identification during the hospitalization. The three classes are hospital-acquired (HA), healthcare-associated (HCA), and community-acquired (CA). Patients with HA-MRSA have MRSA identified at least three days after being admitted. Patients are considered to have HCA-MRSA or CA-MRSA if they were diagnosed with MRSA within two days of their admission. CA-MRSA patients are those who did not have any hospitalizations in the previous year, while HCA-MRSA patients did [19].

Table 1 displays the numbers of different types of new MRSA colonization and infections each month from September 2018 to September 2023 at hospitals in Edmonton, Calgary, rural areas of Alberta and all areas of Alberta. The rate of MRSA patients (number of colonizations or infections per thousand admissions) in different areas of Alberta is also shown. Calgary and Edmonton are two major cities in Alberta, with populations of approximately 1.6 and 1.2 million, respectively, while rural areas comprise the central, south and north regions of the province, with over 0.8 million people living there [21]. MRSA cases in all areas of Alberta summarize the total number of MRSA patients in all Alberta hospitals, both urban and rural.

Table 1.

The monthly number of new MRSA cases in Alberta hospitals

	Edmonton			Calgary			Rural areas			All areas of Alberta
	Mean	Median	Q1 - Q3	Mean	Median	Q1 - Q3	Mean	Median	Q1 - Q3	Mean	Median	Q1 - Q3
HA-MRSA colonization (per 1000 admissions)	24.62 (2.07)	24.00 (2.00)	20.00 - 28.00 (1.73 - 2.26)	7.57 (0.63)	7.00 (0.57)	5.00 - 10.00 (0.42 - 0.80)	7.38 (0.84)	7.00 (0.80)	5.00 - 10.00 (0.60 - 1.09)	39.60 (1.21)	39.00 (1.18)	34.00 - 44.00 (1.06 - 1.29)
HA-MRSA infections (per 1000 admissions)	5.93 (0.50)	6.00 (0.50)	4.00 - 8.00 (0.35 - 0.65)	4.21 (0.35)	4.00 (0.33)	3.00 - 5.00 (0.25 - 0.40)	2.64 (0.30)	2.00 (0.23)	1.00 - 4.00 (0.12 - 0.44)	12.80 (0.39)	12.00 (0.36)	10.00 - 15.00 (0.31 - 0.44)
HCA-MRSA colonization (per 1000 admissions)	15.97 (1.34)	16.00 (1.33)	12.00 - 20.00 (1.04 - 1.61)	13.10 (1.09)	14.00 (1.14)	11.00 - 16.00 (0.93 - 1.28)	15.00 (1.71)	15.00 (1.72)	11.00 - 18.00 (1.32 - 1.97)	44.10 (1.35)	46.00 (1.40)	37.00 - 49.00 (1.15 - 1.44)
HCA-MRSA infections (per 1000 admissions)	5.46 (0.46)	6.00 (0.50)	4.00 - 7.00 (0.35 - 0.57)	3.56 (0.30)	3.00 (0.25)	2.00 - 5.00 (0.17 - 0.40)	3.85 (0.44)	4.00 (0.46)	2.00 - 5.00 (0.24 - 0.55)	12.90 (0.39)	13.00 (0.39)	10.00 - 15.00 (0.31 - 0.44)
CA-MRSA colonization (per 1000 admissions)	30.31 (2.54)	30.00 (2.49)	26.00 - 35.00 (2.24 - 2.83)	9.39 (0.78)	9.00 (0.74)	7.00 - 11.00 (0.59 - 0.88)	19.00 (2.17)	19.00 (2.18)	16.00 - 22.00 (1.91 - 2.41)	58.70 (1.79)	58.00 (1.76)	53.00 - 64.00 (1.65 - 1.88)
CA-MRSA infections (per 1000 admissions)	18.10 (1.52)	17.00 (1.41)	14.00 - 22.00 (1.21 - 1.78)	7.34 (0.61)	7.00 (0.57)	5.00 - 9.00 (0.42 - 0.72)	8.52 (0.97)	8.00 (0.92)	7.00 - 10.00 (0.84 - 1.09)	34.00 (1.04)	34.00 (1.03)	29.00 - 39.00 (0.90 - 1.15)
Admissions	11917.90	12048.00	11588.00 - 12,388.00	12039.98	12228.00	11781.00 - 12,503.00	8769.26	8697.00	8360.00 - 9140.00	32727.15	32915.00	32118.00 - 34,044.00
Discharges	11919.87	12047.00	11547.00 - 12,419.00	12038.77	12289.00	11778.00 - 12,467.00	8774.89	8715.00	8375.00 - 9178.00	32733.52	32906.00	32054.00 - 33,925.00

MRSA: Methicillin-resistant Staphylococcus aureus; HA: Hospital-acquired; HCA: Healthcare-associated; CA: Community-acquired; Q1: The first quartile (the 25th percentile); Q3: The third quartile(the 75th percentile); Study period: September 2018 to September 2023

During the study period, new cases of HA-MRSA colonization outnumbered HA-MRSA infections in all areas of Alberta (Fig. 1). In Edmonton, new HA-MRSA-colonized cases are roughly four times those of infected cases, and they rise significantly in August 2023 before falling. In contrast, the ratio of new colonizations per infections is much lower in Calgary and rural areas (Fig. 1). Most Alberta hospitals also report new cases of HCA-MRSA colonization with high fluctuations, which are over three times the number of HCA-MRSA infections (Fig. 2). Meanwhile, there is a noticeable increase in Edmonton and rural regions throughout the first half of 2019. The trend is also evident in the total number of new HCA-MRSA colonization cases in Alberta.

Fig. 1.

New cases of hospital-acquired (HA) MRSA colonization (left) and infections (right) in hospitals in Edmonton, Calgary, rural areas, and all areas of Alberta

Fig. 2.

New cases of healthcare-associated (HCA) MRSA colonization (left) and infections (right) in hospitals in Edmonton, Calgary, rural areas, and all areas of Alberta

In hospitals across Alberta, the average number of new CA-MRSA colonization cases exceeds the number of CA-MRSA infections (Fig. 3). CA-MRSA patients in hospitals are less common than HCA-MRSA patients in Alberta, but more common than HA-MRSA patients. Furthermore, compared to new cases with CA-MRSA infections, we see greater variability in new instances of CA-MRSA colonization. In April 2020, fewer patients entered and exited hospitals due to the COVID-19 pandemic and facility closures [22]. Aside from that, the number of hospital admissions and discharges follows the same steady trend in all areas of Alberta (Fig. 4). Overall, Edmonton is home to half of the MRSA cases in Alberta, despite accounting for one-third of the province’s hospital admissions and discharges. The proportion of MRSA patients in Calgary and rural areas is similar, with each accounting for one-quarter of all patients.

Fig. 3.

New cases of community-acquired (CA) MRSA colonization (left) and infections (right) in hospitals in Edmonton, Calgary, rural areas, and all areas of Alberta

Fig. 4.

Admissions (left) and discharges (right) in hospitals in Edmonton, Calgary, rural areas, and all areas of Alberta

The Kruskal-Wallis test is used to determine seasonality in data [23], and there are no detectable seasonal differences among these patient categories during the study period (p > 0.05). In addition, even if HCA-MRSA cases have been admitted to hospitals in the last year, there is no guarantee that they were colonized or infected there. Since both HCA-MRSA and CA-MRSA patients are found within two days of admission, they are combined and labelled as CA-MRSA patients. Therefore, our model will contain instances with HA-MRSA or CA-MRSA colonization or infections.

Model of MRSA spread

Model structure. Fig. 5 shows our compartmental model of MRSA dissemination in hospitals. The model structure includes susceptible people (S), patients with HA-MRSA colonization (), patients with HA-MRSA infections (), patients with CA-MRSA colonization (), patients with CA-MRSA infections (), and a cumulative count of MRSA patients who are isolated or via further measures are excluded from the dynamics of MRSA transmission (R).

Fig. 5.

The MRSA transmission model in hospitals. The model includes susceptible people (S), patients with HA-MRSA colonization (), HA-MRSA infections (), CA-MRSA colonization (), CA-MRSA infections (), and isolated patients (R). When susceptible people come into contact with people who have HA-MRSA colonization, HA-MRSA infections, CA-MRSA colonization, and CA-MRSA infections, the rates of new HA-MRSA colonization are , , , and , respectively. The rate at which new HA-MRSA colonization occurs as a result of unidentified cases is σ. Let α indicate the infection rate of HA-MRSA-colonized patients. Patients with HA-MRSA colonization, HA-MRSA infection, CA-MRSA colonization, and CA-MRSA infection typically stay in the hospital for , , , and , respectively, before being moved to isolation rooms

Within the model, the arrows show which way patients migrate between different compartments (Fig. 5). The number of susceptible individuals rises or falls in response to hospital admissions and discharges. More patients get newly colonized with HA-MRSA when susceptible individuals interact with MRSA patients (, , , ). Patients who are colonized with MRSA may get infections if the site of colonization becomes infected. On the basis of whether they were colonized with HA-MRSA or CA-MRSA ( or ), we categorize these patients as having either infection ( or ). Patients who have HA-MRSA colonization (), HA-MRSA infection (), CA-MRSA colonization (), and CA-MRSA infection () may be assigned to separate rooms for isolation [24].

Model parameters. The parameters represent the rates of transmission between patients in various compartments. , , , and are the rates of new colonizations due to patients already have HA-MRSA colonization (), HA-MRSA infections (), CA-MRSA colonization (), and CA-MRSA infections (), respectively (Table 2). σ is the rate of new colonizations due to unidentified MRSA patients. Therefore, the overall transition rate from susceptible persons (S) to HA-MRSA-colonized patients () is . For patients with HA-MRSA colonization (), the rate of infection is α. In general, patients colonized by HA-MRSA (), infected by HA-MRSA (), colonized by CA-MRSA (), or infected by CA-MRSA () will remain in hospitals for some time before being moved to isolated rooms. Under our model, we assume the inverse of their typical lengths of stay are , , , and , respectively (Table 3). We suppose that patients enter and remain in the removal (R) while they are segregated. The R compartment finally contains everyone who was colonized or infected with MRSA throughout the study. We do not need to model the rate at which patients leave isolation, as we assume they have no more effect on MRSA transmission once they have entered isolation.

Table 2.

MRSA transmission model parameters and their priors

Parameter	Notation	Prior 1	Prior 2	Prior 3
Transmission rate. Direct contact between susceptible people and HA-MRSA-colonized patients can lead to new HA-MRSA colonization.
Transmission rate. Direct contact between susceptible people and HA-MRSA-infected patients can lead to new HA-MRSA colonization.
Transmission rate. Direct contact between susceptible people and CA-MRSA-colonized patients can lead to new HA-MRSA colonization.
Transmission rate. Direct contact between susceptible people and CA-MRSA-infected patients can lead to new HA-MRSA colonization.
Import parameter. Direct contact between susceptible people and MRSA patients who are not identified can lead to new HA-MRSA colonization.	σ
Infection rate. Infection may occur in patients with HA-MRSA colonization.	α

Table 3.

MRSA transmission model parameters with their values

Parameter	Notation	Value	Source
Inverse time to send to isolated rooms. Prior to being placed under isolation, patients with HA-MRSA colonization often stay in hospitals for days.		1.3	[25]
Inverse time to send to isolated rooms. Prior to being placed under isolation, patients with HA-MRSA infection often stay in hospitals for days.		1.3	[25]
Inverse time to send to isolated rooms. Prior to being placed under isolation, patients with CA-MRSA colonization often stay in hospitals for days.		10	[19]
Inverse time to send to isolated rooms. Prior to being placed under isolation, patients with CA-MRSA infection often stay in hospitals for days.		10	[19]

MRSA transmission dynamics. Let , τ = 61 represent the number of months in the research period. At time (or month) t, the number of susceptible people is denoted by . Likewise, , , , , and denote the number of patients in the HA-MRSA colonization, HA-MRSA infection, CA-MRSA colonization, CA-MRSA infection, and isolated (removed) compartment at time t, respectively. is the entire number of individuals included in the study at time t, in other words, . Further, let represent new HA-MRSA-colonized patients, represent new HA-MRSA-infected patients, represent new CA-MRSA-colonized patients, represent new CA-MRSA-infected patients. , , , and indicate patients who are transferred to hospital isolated rooms for each of the following patient groups: HA-MRSA colonization, HA-MRSA infection, CA-MRSA colonization, and CA-MRSA infection, respectively. The overall number of persons () and susceptible people () at time t+1 may be affected by admission to the hospital () and release () at time t. The following difference equations then illustrate the movement of patients between different compartments in hospitals:

Let be the probability that a susceptible person will become a new colonized patient in a hospital. Let be the probability that a HA-MRSA-colonized patient will become infected. Regarding patients in the HA-MRSA colonization, HA-MRSA infection, CA-MRSA colonization, and CA-MRSA infection compartments, the corresponding transition probabilities to isolation are , , , and . In our model, these probabilities are given as:

All parameters, will be estimated except , , , and , because we lack data on isolated cases. Therefore, we need to determine how frequently certain types of MRSA cases are isolated beforehand. It would typically take a few days for medical staff to identify admitted individuals once they have interacted with MRSA patients and become colonized, and send them to different rooms. We assume that this procedure will take three weeks for HA-MRSA, so we set and equal to 1.3 [25]. We assume that patients with CA-MRSA (colonization or infections) will be detected within two days of their arrival based on current microbiologic identification, and relocated to segregated wards on the third day. Thus, and are set equal to 10 [19]. Then the number of new patients entering each of , , , , , , , and is given by:

We let be a parameter vector containing parameters to be estimated (see Table 2). Let represent a parameter vector that includes assumed parameters (see Table 3). The likelihood function is given by:

We use to represent our data. The starting value of susceptible individuals () is the quantity of beds in acute care hospitals in Alberta. (The number of acute care beds: All Alberta: 8605; Edmonton: 3048; Calgary: 2855; rural Alberta: 2702.) The number of new MRSA patients in September 2018 is the first entry in the compartments for HA-MRSA colonization (), HA-MRSA infection (), CA-MRSA colonization (), and CA-MRSA infection (), respectively. R is assumed to be zero at time t=0.

Bayesian inference and Markov chain Monte Carlo (MCMC) methods

To estimate model parameters in the study, we use a Bayesian framework and Metropolis-Hastings Markov chain Monte Carlo (MCMC) methods [26]. The prior density P(Θ) represents our beliefs regarding the parameters before seeing the data D. After taking into account the observed data, our updated belief regarding the parameters is represented by the posterior density P(Θ|D). The posterior is proportional to the likelihood function multiplied by the prior [27], i.e., . Here, we consider weakly informative priors, which increase the dependence of the posterior on the observed data. To determine how sensitive the posterior mean estimate is to prior assumptions, we consider three independent gamma priors (, , and ) for each of our rate parameters (Table 2).

A package nimble [28–30] in R [31], v4.4.1] is used to draw samples from the posterior using MCMC. The chains are run for 60,000 iterations with an initial burn-in of 10,000 iterations removed. Convergence is assessed visually using trace plots.

Additional MRSA-colonized cases upon admission

Initially, the model is fitted to data from hospitals in all areas of Alberta, and the posterior mean of transmission parameters is estimated. The model is then fitted with data from hospitals in different areas of Alberta. These include hospitals in Edmonton, Calgary, and rural Alberta.

In the model framework, new cases of HA-MRSA infections are assumed to arise from HA-MRSA-colonized patients because some HA-MRSA-colonized patients may develop infections in hospitals, but data from Calgary and rural Alberta hospitals show that the amount of HA-MRSA-colonized patients is slightly lower than the number of new HA-MRSA-infected patients over a few months (1–4 cases lower). This could be because some patients admitted to hospitals may have been colonized with MRSA prior to admission [15], which are omitted from our model and data. We then hypothesize that a certain proportion of people admitted to hospitals are colonized with MRSA [12, 13], but these patients are not recognized on the first or second day of admission due to a suboptimal screening rate (66%-86%) [32], so these colonized patients are assumed to be new cases of HA-MRSA colonization as they are identified at least three days after admission [19].

Let λ be the prevalence of individuals on admission who are colonized with MRSA, and this prevalence is assumed to range from 0.0008 to 0.0012, i.e., 0.8 to 1.2 MRSA-colonized cases per 1000 admissions to hospitals [7]. Introducing unidentified colonized cases upon admission may marginally lower the number of admitted susceptible persons while slightly increasing the number of HA-MRSA-colonized patients in hospitals:

To assess the impact of assumed additional MRSA-colonized cases on the transmission rate in hospitals, we consider several values of λ with a 0.0001 increase in model fitting to data from hospitals in Calgary and rural Alberta, i.e., , 0.0009, 0.0010, 0.0011, 0.0012. When fitting our model to datasets from hospitals in all areas of Alberta, we use λ = 0, 0.0008, 0.0009, 0.0010, 0.0011, 0.0012, because the model can be fitted without making assumptions about hidden colonizations. When fitting the model to data from Edmonton hospitals, we employ λ = 0, 0.0008, 0.0009, 0.0010, 0.0011, because the assumption λ = 0.0012 is not appropriate for data from Edmonton hospitals and the number of new HA-MRSA colonizations will exceed the number of susceptible individuals near the end of time. This also demonstrates that the percentage of people who are colonized upon hospital admission in Alberta may be very low. Therefore, maintaining λ at a low value can not only assess how unidentified colonized patients affect MRSA transmission in hospitals, but it also has little effect on the actual transmission rate. Furthermore, the introduction of unidentified colonized patients (λ) is expected to marginally raise the transmission rate between susceptible people and unidentified cases (σ).

Results

The posterior mean estimates of the parameters with their 95% credible intervals (CIs), based on patient data from hospitals in all areas of Alberta, Edmonton, Calgary and rural areas of Alberta, respectively, are shown in Tables 4 to 5. Figures 6, 7, 8, 9 show the posterior mean estimates of model parameters in different areas of Alberta when the number of unidentified MRSA-colonized patients is varied from 0.8 per 1000 admissions to 1.2 per 1000 admissions. We use notation and represent the posterior mean estimates of and , respectively.

Table 4.

Parameter estimates with 95% credible intervals (CIs) using data from hospitals in all of Alberta

	Prior 1:
λ
0	0.0291 (0.0008, 0.1005)	0.0778 (0.0022, 0.2780)	0.0094 (0.0002, 0.0333)	0.0526 (0.0013, 0.1823)	0.0050 (0.0044, 0.0054)	0.4230 (0.3939, 0.4542)
0.0008	0.0088 (0.0001, 0.0333)	0.0690 (0.0019, 0.2487)	0.0054 (0.0001, 0.0201)	0.0463 (0.0012, 0.1645)	0.0114 (0.0108, 0.0119)	0.1912 (0.1778, 0.2050)
0.0009	0.0081 (0.0002, 0.0295)	0.0689 (0.0019, 0.2508)	0.0051 (0.0001, 0.0188)	0.0485 (0.0012, 0.1741)	0.0124 (0.0118, 0.0130)	0.1785 (0.1661, 0.1914)
0.0010	0.0073 (0.0001, 0.0269)	0.0659 (0.0017, 0.2404)	0.0049 (0.0001, 0.0183)	0.0501 (0.0012, 0.1840)	0.0136 (0.0129, 0.0141)	0.1681 (0.1564, 0.1800)
0.0011	0.0067 (0.0001, 0.0253)	0.0672 (0.0017, 0.2408)	0.0045 (0.0001, 0.0165)	0.0522 (0.0013, 0.1902)	0.0148 (0.0141, 0.0153)	0.1589 (0.1478, 0.1701)
0.0012	0.0063 (0.0001, 0.0233)	0.0746 (0.0018, 0.2694)	0.0044 (0.0001, 0.0164)	0.0543 (0.0014, 0.1906)	0.0160 (0.0153, 0.0166)	0.1513 (0.1409, 0.1622)
	Prior 2:
λ
0	0.0299 (0.0008, 0.1047)	0.0829 (0.0025, 0.2799)	0.0095 (0.0002, 0.0337)	0.0525 (0.0014, 0.1839)	0.0050 (0.0044, 0.0054)	0.4231 (0.3937, 0.4535)
0.0008	0.0089 (0.0002, 0.0327)	0.0730 (0.0021, 0.2596)	0.0053 (0.0001, 0.0192)	0.0498 (0.0014, 0.1763)	0.0114 (0.0108, 0.0119)	0.1912 (0.1777, 0.2048)
0.0009	0.0080 (0.0002, 0.0294)	0.0737 (0.0019, 0.2664)	0.0051 (0.0001, 0.0186)	0.0517 (0.0014, 0.1862)	0.0124 (0.0117, 0.0129)	0.1786 (0.1661, 0.1914)
0.0010	0.0073 (0.0001, 0.0268)	0.0728 (0.0021, 0.2648)	0.0048 (0.0001, 0.0174)	0.0542 (0.0014, 0.1985)	0.0135 (0.0129, 0.0141)	0.1681 (0.1562, 0.1802)
0.0011	0.0066 (0.0001, 0.0242)	0.0705 (0.0015, 0.2538)	0.0047 (0.0001, 0.0169)	0.0555 (0.0012, 0.1985)	0.0147 (0.0140, 0.0153)	0.1589 (0.1481, 0.1702)
0.0012	0.0062 (0.0001, 0.0228)	0.0776 (0.0020, 0.2793)	0.0044 (0.0001, 0.0166)	0.0574 (0.0013, 0.2101)	0.0160 (0.0153, 0.0166)	0.1513 (0.1409, 0.1622)
	Prior 3:
0	0.0302 (0.0008, 0.1059)	0.0865 (0.0020, 0.2983)	0.0096 (0.0002, 0.0343)	0.0553 (0.0015, 0.1921)	0.0049 (0.0044, 0.0054)	0.4231 (0.3934, 0.4538)
0.0008	0.0089 (0.0002, 0.0328)	0.0762 (0.0020, 0.2765)	0.0053 (0.0001, 0.0196)	0.0504 (0.0012, 0.1848)	0.0114 (0.0107, 0.0119)	0.1914 (0.1781, 0.2053)
0.0009	0.0080 (0.0002, 0.0294)	0.0759 (0.0018, 0.2871)	0.0051 (0.0001, 0.0186)	0.0507 (0.0014, 0.1843)	0.0124 (0.0117, 0.0129)	0.1786 (0.1661, 0.1915)
0.0010	0.0074 (0.0001, 0.0281)	0.0739 (0.0018, 0.2681)	0.0048 (0.0001, 0.0180)	0.0533 (0.0014, 0.1973)	0.0135 (0.0128, 0.0141)	0.1681 (0.1564, 0.1801)
0.0011	0.0068 (0.0001, 0.0253)	0.0737 (0.0020, 0.2663)	0.0047 (0.0001, 0.0174)	0.0546 (0.0014, 0.1989)	0.0147 (0.0140, 0.0153)	0.1589 (0.1477, 0.1702)
0.0012	0.0064 (0.0001, 0.0235)	0.0820 (0.0017, 0.2956)	0.0046 (0.0001, 0.0170)	0.0574 (0.0014, 0.2069)	0.0160 (0.0152, 0.0166)	0.1513 (0.1406, 0.1622)

λ : The proportion of colonized individuals upon admission;Θ = (βCH, βIH, βCC, βIC, σ, α)⊺ : The vector of model parameters is estimated using different priors

Table 5.

Parameter estimates with 95% credible intervals (CIs) using data from hospitals in rural areas

	Prior 1:
λ
0.0008	0.0385 (0.0009, 0.1370)	0.2190 (0.0069, 0.7223)	0.0252 (0.0007, 0.0865)	0.1143 (0.0039, 0.3800)	0.0070 (0.0058, 0.0080)	0.1697 (0.1447, 0.1967)
0.0009	0.0345 (0.0009, 0.1210)	0.2247 (0.0059, 0.7349)	0.0235 (0.0006, 0.0826)	0.1143 (0.0034, 0.3669)	0.0078 (0.0067, 0.0088)	0.1587 (0.1351, 0.1839)
0.0010	0.0301 (0.0007, 0.1094)	0.2036 (0.0064, 0.6949)	0.0211 (0.0006, 0.0758)	0.1093 (0.0031, 0.3665)	0.0087 (0.0076, 0.0097)	0.1467 (0.1248, 0.1703)
0.0011	0.0274 (0.0007, 0.0996)	0.2010 (0.0055, 0.6720)	0.0190 (0.0004, 0.0680)	0.1103 (0.0032, 0.3712)	0.0097 (0.0085, 0.0106)	0.1365 (0.1162, 0.1584)
0.0012	0.0255 (0.0005, 0.0940)	0.1927 (0.0055, 0.6739)	0.0183 (0.0005, 0.0650)	0.1122 (0.0033, 0.3848)	0.0105 (0.0092, 0.0114)	0.1296 (0.1103, 0.1504)
	Prior 2:
λ
0.0008	0.0408 (0.0010, 0.1425)	0.2664 (0.0080, 0.8378)	0.0249 (0.0006, 0.0858)	0.1238 (0.0042, 0.3992)	0.0070 (0.0057, 0.0079)	0.1698 (0.1441, 0.1974)
0.0009	0.0355 (0.0009, 0.1232)	0.2712 (0.0086, 0.8733)	0.0230 (0.0006, 0.0794)	0.1261 (0.0037, 0.4088)	0.0077 (0.0065, 0.0087)	0.1590 (0.1354, 0.1843)
0.0010	0.0310 (0.0008, 0.1110)	0.2450 (0.0075, 0.8083)	0.0212 (0.0005, 0.0757)	0.1201 (0.0032, 0.4029)	0.0086 (0.0074, 0.0096)	0.1470 (0.1250, 0.1706)
0.0011	0.0275 (0.0006, 0.0986)	0.2424 (0.0071, 0.8083)	0.0198 (0.0005, 0.0702)	0.1227 (0.0037, 0.4095)	0.0096 (0.0083, 0.0106)	0.1368 (0.1165, 0.1587)
0.0012	0.0262 (0.0006, 0.0942)	0.2411 (0.0077, 0.8117)	0.0186 (0.0005, 0.0680)	0.1214 (0.0034, 0.4041)	0.0104 (0.0091, 0.0114)	0.1298 (0.1102, 0.1510)
	Prior 3:
λ
0.0008	0.0412 (0.0009, 0.1460)	0.2773 (0.0081, 0.8549)	0.0257 (0.0006, 0.0919)	0.1270 (0.0035, 0.3969)	0.0069 (0.0057, 0.0079)	0.1698 (0.1447, 0.1970)
0.0009	0.0375 (0.0009, 0.1332)	0.2844 (0.0078, 0.9081)	0.0233 (0.0006, 0.0818)	0.1288 (0.0038, 0.4160)	0.0077 (0.0064, 0.0087)	0.1593 (0.1355, 0.1854)
0.0010	0.0313 (0.0007, 0.1106)	0.2631 (0.0075, 0.8507)	0.0211 (0.0004, 0.0758)	0.1270 (0.0038, 0.4141)	0.0086 (0.0073, 0.0096)	0.1469 (0.1249, 0.1706)
0.0011	0.0282 (0.0007, 0.1042)	0.2566 (0.0077, 0.8661)	0.0195 (0.0004, 0.0690)	0.1275 (0.0046, 0.4202)	0.0095 (0.0082, 0.0106)	0.1367 (0.1163, 0.1585)
0.0012	0.0257 (0.0006, 0.0902)	0.2532 (0.0074, 0.8301)	0.0183 (0.0004, 0.0645)	0.1275 (0.0035, 0.4252)	0.0103 (0.0091, 0.0114)	0.1298 (0.1101, 0.1505)

λ : The proportion of colonized individuals upon admission;Θ = (βCH, βIH, βCC, βIC, σ, α)⊺ : The vector of model parameters is estimated using different priors

Fig. 6.

Changes in the posterior mean estimates of model parameters with their 95% credible intervals (CIs) using data from hospitals in all areas of Alberta, assuming 0.8 to 1.2 colonized cases per 1000 admissions with different priors

Fig. 7.

Changes in the posterior mean estimates of model parameters with their 95% credible intervals (CIs) using data from hospitals in rural areas, assuming 0.8 to 1.2 colonized cases per 1000 admissions with different priors

Fig. 8.

Changes in the posterior mean estimates of model parameters with their 95% credible intervals (CIs) using data from Edmonton hospitals, assuming 0.8 to 1.1 colonized cases per 1000 admissions with different priors

Fig. 9.

Changes in the posterior mean estimates of model parameters with their 95% credible intervals (CIs) using data from Calgary hospitals, assuming 0.8 to 1.2 colonized cases per 1000 admissions with different priors

Data from hospitals in all areas of Alberta

We first consider posterior mean estimates when fitting the model to data from hospitals in all areas of Alberta (Table 4). Initially, we do not include further unreported colonized cases upon admission because the model can accommodate the original data.

Using prior 1, we see that a patient colonized with HA-MRSA () usually colonizes 0.029 (95% CI: (0.001, 0.101)) susceptible people each month with each contact. On average, a patient infected with HA-MRSA () colonizes 0.078 (95% CI: (0.002, 0.278)) susceptible people per interaction each month. In the meantime, an average of 0.009 (95% CI: (0.000, 0.033)) susceptible people become colonized when a CA-MRSA-colonized patient () interacts with susceptible people per month. Under the posterior mean, every interaction between a CA-MRSA-infected patient () and a susceptible individual results in an average of 0.053 (95% CI: (0.001, 0.182)) susceptible individuals being colonized with HA-MRSA every month. Moreover, each contact with an undetected MRSA case () colonizes an average of 0.005 (95% CI: (0.004, 0.005)) susceptible people monthly. The infection rate () for HA-MRSA colonized patients is approximately 0.423 (95% CI: (0.394, 0.454)). Under the other two priors, we find that the posterior mean estimates of parameters are similar.

Next, we consider the model under the assumption that there are 0.8 unobserved colonized cases for every 1000 admissions. As we can see, , , , and drop to 0.009, 0.069, 0.005, and 0.046, respectively. Conversely, rises from 0.005 to 0.011, suggesting that more susceptible people are colonized with MRSA in hospitals by unidentified MRSA patients. As more patients colonized with MRSA in hospitals are added to the data, the infection rate declines to 0.191.

The changes in parameter estimates when we adjust the MRSA colonization rate among hospital admissions in all areas of Alberta can be seen in Fig. 6. When we change the assumption that there are 0.8 colonized cases per 1000 admissions to 0.9 colonized cases per 1000 admissions (λ= 0.0009), decreases and its percentage change is −8%, compared to its posterior mean estimate when λ= 0.0008 using prior 1, and the percentage change of , , , , and are around 0%, −4%, 5%, 9%, and −7%, respectively. (When λ= 0.0009, 0.0010, 0.0011, and 0.0012, the percentage change in posterior mean estimates compared to λ= 0.0008 are: : −8%, −17%, −23%, −29%; : 0%, −5%, −3%, 8%; : −4%, −9%, −16%, −18%; : 5%, 8%, 13%, 17%; : 9%, 19%, 29%, 41%; : −7%, −12%, −17%, −21%.) Using the alternative priors results in similar posterior estimates.

We find that and progressively decrease as the prevalence of MRSA-colonized individuals upon admission λ rises from 0.0008 to 0.0012, suggesting that fewer susceptible individuals per contact every month for every MRSA-colonized patient are colonized. As marginally increases, MRSA-infected patients colonize more susceptible people with each monthly interaction. The increase in suggests that more susceptible people would likewise be colonized by unidentified MRSA patients. We also see that as there are more colonized patients rather than infections, the infection rate falls.

Data from Edmonton hospitals

Table 6 displays the posterior mean estimations of parameters based on data from Edmonton hospitals. First, we exclude additional unreported colonized cases from admissions.

Table 6.

Parameter estimates with 95% credible intervals (CIs) using data from Edmonton hospitals

	Prior 1:
λ
0	0.0446 (0.0010, 0.1608)	0.0589 (0.0017, 0.2107)	0.0091 (0.0002, 0.0336)	0.0398 (0.0011, 0.1449)	0.0099 (0.0090, 0.0107)	0.2631 (0.2368, 0.2909)
0.0008	0.0153 (0.0003, 0.0560)	0.0479 (0.0013, 0.1736)	0.0075 (0.0001, 0.0275)	0.0433 (0.0012, 0.1571)	0.0196 (0.0185, 0.0206)	0.1632 (0.1469, 0.1805)
0.0009	0.0139 (0.0003, 0.0522)	0.0461 (0.0011, 0.1709)	0.0072 (0.0002, 0.0257)	0.0431 (0.0012, 0.1563)	0.0212 (0.0201, 0.0222)	0.1561 (0.1404, 0.1725)
0.0010	0.0134 (0.0003, 0.0509)	0.0455 (0.0011, 0.1684)	0.0069 (0.0001, 0.0245)	0.0463 (0.0012, 0.1717)	0.0230 (0.0218, 0.0241)	0.1497 (0.1349, 0.1658)
0.0011	0.0123 (0.0003, 0.0455)	0.0448 (0.0010, 0.1663)	0.0067 (0.0001, 0.0251)	0.0464 (0.0012, 0.1726)	0.0248 (0.0236, 0.0260)	0.1436 (0.1291, 0.1589)
	Prior 2:
λ
0	0.0439 (0.0010, 0.1584)	0.0611 (0.0016, 0.2130)	0.0097 (0.0002, 0.0358)	0.0420 (0.0012, 0.1539)	0.0099 (0.0090, 0.0106)	0.2632 (0.2362, 0.2909)
0.0008	0.0158 (0.0003, 0.0590)	0.0498 (0.0014, 0.1879)	0.0074 (0.0001, 0.0274)	0.0460 (0.0012, 0.1732)	0.0196 (0.0185, 0.0205)	0.1634 (0.1469, 0.1806)
0.0009	0.0145 (0.0003, 0.0542)	0.0478 (0.0012, 0.1764)	0.0072 (0.0001, 0.0258)	0.0468 (0.0010, 0.1727)	0.0212 (0.0201, 0.0222)	0.1561 (0.1405, 0.1727)
0.0010	0.0139 (0.0003, 0.0512)	0.0485 (0.0012, 0.1808)	0.0069 (0.0002, 0.0250)	0.0477 (0.0012, 0.1725)	0.0230 (0.0218, 0.0241)	0.1498 (0.1343, 0.1656)
0.0011	0.0121 (0.0003, 0.0448)	0.0475 (0.0010, 0.1796)	0.0068 (0.0002, 0.0243)	0.0479 (0.0010, 0.1748)	0.0248 (0.0236, 0.0259)	0.1437 (0.1293, 0.1589)
	Prior 3:
λ
0	0.0437 (0.0009, 0.1549)	0.0610 (0.0017, 0.2149)	0.0096 (0.0002, 0.0352)	0.0437 (0.0009, 0.1588)	0.0099 (0.0090, 0.0106)	0.2631 (0.2367, 0.2913)
0.0008	0.0155 (0.0003, 0.0559)	0.0500 (0.0012, 0.1840)	0.0077 (0.0001, 0.0286)	0.0456 (0.0011, 0.1628)	0.0196 (0.0185, 0.0205)	0.1635 (0.1473, 0.1805)
0.0009	0.0144 (0.0003, 0.0550)	0.0495 (0.0013, 0.1804)	0.0072 (0.0001, 0.0268)	0.0471 (0.0011, 0.1677)	0.0212 (0.0201, 0.0222)	0.1564 (0.1407, 0.1726)
0.0010	0.0135 (0.0003, 0.0512)	0.0491 (0.0012, 0.1820)	0.0070 (0.0001, 0.0256)	0.0469 (0.0013, 0.1732)	0.0230 (0.0218, 0.0241)	0.1498 (0.1348, 0.1657)
0.0011	0.0119 (0.0002, 0.0434)	0.0467 (0.0013, 0.1733)	0.0069 (0.0001, 0.0258)	0.0491 (0.0013, 0.1781)	0.0248 (0.0236, 0.0259)	0.1437 (0.1293, 0.1587)

λ : The proportion of colonized individuals upon admission;Θ = (βCH, βIH, βCC, βIC, σ, α)⊺ : The vector of model parameters is estimated using different priors

Using prior 1, we see that patients with HA-MRSA colonization colonize () an average of 0.045 (95% CI: (0.001, 0.161)) susceptible people each month with each contact. Under the posterior mean, every interaction between a patient with HA-MRSA infection () and a susceptible individual results in an average of 0.059 (95% CI: (0.002, 0.211)) susceptible people being colonized with HA-MRSA every month. Meanwhile, an average of 0.009 (95% CI: (0.000, 0.034)) susceptible people are colonized with HA-MRSA when a CA-MRSA-colonized patient () has contact with susceptible people each month. A CA-MRSA-infected patient () colonizes an average of 0.040 (95% CI: (0.001, 0.145)) susceptible people per interaction each month. Moreover, each contact with unobserved colonized cases () results in the colonization of an average of 0.010 (95% CI: (0.009, 0.011)) susceptible individuals every month. Additionally, the average of infection rate () of HA-MRSA colonized patients is 0.263 (95% CI: (0.237, 0.291)). The posterior mean estimates of parameters are quite similar under the other two priors.

Then we make the same assumption that there are 0.8 unobserved colonized cases per 1000 admissions. When the model fits the data again, , , and decrease while increases. It indicates that transmission rates between CA-MRSA-infected patients and susceptible people are slightly higher than for other patient groups. Meanwhile, increases, implying that more susceptible people are colonized with MRSA in hospitals by unidentified patients. The infection rate declines as the amount of hospitalized colonized patients rises.

Adjusting the MRSA colonization rate among hospital admissions throughout Edmonton results in a change in parameter estimations, as shown in Fig. 7. It is assumed that there are 0.8 to 1.1 colonized cases for every thousand admissions (i.e., here λ ranges from 0.0008 to 0.0011). When λ increases from 0.0008 to 0.0009 using prior 1, decreases with a percentage change of −9%. The percentage change of , , , , and are around −4%, −3%, 0%, 8%, and −4%, respectively, compared to their posterior mean estimates when λ= 0.0008. (When λ= 0.0009, 0.0010, and 0.0011, the percentage change in posterior mean estimates compared to λ= 0.0008 are: : −9%, −12%, −20%; : −4%, −5%, −6%; : −3%, −8%, −11%; : 0%, 6.9%, 7.2%; : 8%, 17%, 27%; : −4%, −8%, −12%.) The posterior estimates are similar when alternative priors are used.

We observe that and gradually decline when λ increases, indicating that MRSA-colonized patients colonize fewer susceptible persons per contact each month. Although decreases, the posterior mean estimate is greater than and . Meanwhile, the slight increase in suggests that MRSA-infected patients may colonize more susceptible individuals with each interaction each month. The rise in implies that unidentified MRSA patients would also colonize more susceptible individuals. In addition, the infection rate decreases when there are more colonized patients than infections.

Data from Calgary hospitals

We then examine the posterior mean estimates of the model parameters using data from hospitals in Calgary (Table 7).

Table 7.

Parameter estimates with 95% credible intervals (CIs) using data from Calgary hospitals

	Prior 1:
λ
0.0008	0.0360 (0.0010, 0.1262)	0.4328 (0.0181, 1.1516)	0.0347 (0.0009, 0.1224)	0.1817 (0.0067, 0.5437)	0.0072 (0.0055, 0.0085)	0.2587 (0.2281, 0.2916)
0.0009	0.0334 (0.0008, 0.1222)	0.6042 (0.0374, 1.4604)	0.0332 (0.0009, 0.1152)	0.1943 (0.0074, 0.5759)	0.0079 (0.0060, 0.0094)	0.2332 (0.2054, 0.2624)
0.0010	0.0310 (0.0007, 0.1114)	0.6891 (0.0443, 1.5805)	0.0332 (0.0008, 0.1192)	0.2121 (0.0069, 0.6420)	0.0088 (0.0067, 0.0104)	0.2133 (0.1882, 0.2407)
0.0011	0.0282 (0.0006, 0.1020)	0.8785 (0.0827, 1.8843)	0.0301 (0.0008, 0.1075)	0.2634 (0.0118, 0.7273)	0.0094 (0.0071, 0.0113)	0.1953 (0.1718, 0.2201)
0.0012	0.0264 (0.0006, 0.0972)	1.0922 (0.1290, 2.2220)	0.0293 (0.0008, 0.1071)	0.3074 (0.0124, 0.8640)	0.0102 (0.0076, 0.0123)	0.1826 (0.1611, 0.2054)
	Prior 2:
λ
0.0008	0.0386 (0.0010, 0.1343)	0.5526 (0.0319, 1.3524)	0.0359 (0.0010, 0.1252)	0.1979 (0.0064, 0.5717)	0.0070 (0.0052, 0.0084)	0.2587 (0.2276, 0.2912)
0.0009	0.0339 (0.0008, 0.1167)	0.7414 (0.0679, 1.6459)	0.0351 (0.0010, 0.1247)	0.2255 (0.0089, 0.6739)	0.0076 (0.0056, 0.0092)	0.2334 (0.2061, 0.2630)
0.0010	0.0326 (0.0009, 0.1170)	0.8604 (0.0836, 1.8460)	0.0339 (0.0009, 0.1186)	0.2355 (0.0095, 0.6746)	0.0084 (0.0063, 0.0102)	0.2134 (0.1882, 0.2403)
0.0011	0.0296 (0.0007, 0.1084)	1.1249 (0.1816, 2.2169)	0.0331 (0.0008, 0.1197)	0.2990 (0.0119, 0.8005)	0.0089 (0.0064, 0.0109)	0.1956 (0.1723, 0.2204)
0.0012	0.0270 (0.0007, 0.0982)	1.3611 (0.3128, 2.4795)	0.0312 (0.0008, 0.1120)	0.3573 (0.0166, 0.9394)	0.0096 (0.0070, 0.0119)	0.1824 (0.1607, 0.2051)
	Prior 3:
λ
0.0008	0.0386 (0.0011, 0.1372)	0.5910 (0.0372, 1.4146)	0.0383 (0.0009, 0.1336)	0.2157 (0.0070, 0.6264)	0.0068 (0.0049, 0.0083)	0.2589 (0.2281, 0.2916)
0.0009	0.0346 (0.0008, 0.1262)	0.7872 (0.0659, 1.7229)	0.0342 (0.0008, 0.1246)	0.2337 (0.0082, 0.6694)	0.0075 (0.0054, 0.0092)	0.2334 (0.2058, 0.2625)
0.0010	0.0315 (0.0008, 0.1149)	0.9149 (0.1031, 1.9237)	0.0348 (0.0009, 0.1239)	0.2590 (0.0106, 0.7285)	0.0083 (0.0059, 0.0101)	0.2135 (0.1882, 0.2403)
0.0011	0.0291 (0.0007, 0.1061)	1.1072 (0.1899, 2.1787)	0.0323 (0.0007, 0.1176)	0.3078 (0.0125, 0.8247)	0.0089 (0.0066, 0.0109)	0.1957 (0.1721, 0.2205)
0.0012	0.0267 (0.0007, 0.0990)	1.3784 (0.3056, 2.4854)	0.0312 (0.0007, 0.1122)	0.3531 (0.0160, 0.9452)	0.0096 (0.0069, 0.0118)	0.1826 (0.1611, 0.2053)

λ : The proportion of colonized individuals upon admission;Θ = (βCH, βIH, βCC, βIC, σ, α)⊺ : The vector of model parameters is estimated using different priors

Using prior 1, indicates that each HA-MRSA-colonized patient colonizes an average of 0.036 (95% CI: (0.001, 0.126)) susceptible persons by each contact each month, supposing that there are 0.8 colonized cases for every 1000 admissions. Likewise, means that for every contact with a patient with HA-MRSA infections, an average of 0.433 (95% CI: (0.018, 1.152)) susceptible individuals become new HA-MRSA-colonized patients each month. On average, a CA-MRSA-colonized patient () colonizes 0.035 (95% CI: (0.001, 0.122)) susceptible people monthly with each contact, and a CA-MRSA-infected patient () typically colonizes an average of 0.182 (95% CI: (0.007, 0.544)) susceptible individuals every month per contact. Under the posterior mean, an average of 0.007 (95% CI: (0.006, 0.009)) susceptible individuals are colonized by one unobserved MRSA patient () per contact every month. Furthermore, the infection rate () for HA-MRSA-colonized patients is approximately 0.259 (95% CI: (0.228, 0.292)). Under the other two priors, the posterior mean estimates of parameters are similar and their 95% CIs almost overlap.

Figure 8 shows how parameter estimates rise or fall when the MRSA prevalence rate among patients admitted to Calgary hospitals rises. When λ increases from 0.0008 to 0.0009 using prior 1, decreases and the percentage change is about −7%. The percentage change of , , , , and are roughly 40%, −5%, 7%, 10%, and −10%, respectively, compared to their posterior mean estimates when λ= 0.0008. (When λ= 0.0009, 0.0010, 0.0011, and 0.0012, the percentage change in posterior mean estimates compared to λ= 0.0008 are: : −7%, −14%, −22%, −27%; : 40%, 59%, 103%, 152%; : −5%, −5%, −13%, −16%; : 7%, 17%, 45%, 69%; : 10%, 21%, 30%, 41%; : −10%, −18%, −25%, −29%.) The posterior estimates using various priors are similar when assuming that more patients are colonized with MRSA upon admission.

We find that and decline, but and noticeably increase when the prevalence of unidentified MRSA-colonized patients λ is increased from 0.0008 to 0.0012. The number of susceptible people slightly diminishes when some admissions are MRSA-colonized cases, and the transmission rates between susceptible people and MRSA-colonized patients also drop. However, the MRSA transmission rates between susceptible people and MRSA-infected patients rise, which would suggest that MRSA-infected patients are more likely to spread MRSA in Calgary hospitals. Meanwhile, since it is expected that there are more undetected MRSA patients who will spread MRSA to susceptible individuals, also increases. The infection rate falls when we only assume that a small percentage of patients are admitted with MRSA colonization, while the total number of MRSA infections stays constant.

Data from hospitals in rural areas

The posterior mean estimates of the parameters are then examined using data from hospitals in rural areas (Table 5).

The model first fits the data using prior 1 and assumes that MRSA colonization occurs in 0.8 of 1000 admissions. We find that 0.039, meaning that every month, an average of 0.039 (95% CI: (0.001, 0.137)) susceptible people become colonized every time a patient with HA-MRSA colonization interacts with susceptible individuals. Similarly, a patient infected with HA-MRSA () typically colonizes an average of 0.219 (95% CI: (0.007, 0.722)) susceptible individuals per contact per month. An average of 0.025 (95% CI: (0.001, 0.087)) susceptible people become new HA-MRSA-colonized patients every month for each interaction with a patient who has CA-MRSA colonization (). On average, a CA-MRSA-infected patient () colonizes 0.114 (95% CI: (0.004, 0.380)) susceptible individuals every month with each interaction. Under the posterior mean, every contact with an unobserved MRSA patient () colonizes an average of 0.007 (95% CI: (0.006, 0.008)) susceptible individuals per month. Patients with HA-MRSA colonization have an infection rate () of around 0.170 (95% CI: (0.145, 0.197)). The posterior mean estimates of the parameters are comparable under the other two priors, and their 95% CIs nearly overlap.

When we alter the MRSA colonization rate among hospital admissions in rural Alberta, Fig. 9 displays the change in parameter estimations. When λ rises from 0.0008 to 0.0009 using prior 1, declines and its percentage change is about −10%. The change of , , , , and are about 3%, −7%, 0%, 11%, and −6%, respectively, compared to their posterior mean estimates when λ= 0.0008. (When λ= 0.0009, 0.0010, 0.0011, and 0.0012, the percentage change in posterior mean estimates compared to λ= 0.0008 are: : −10%, −22%, −29%, −34%; : 3%, −7%, −8%, −12%; : −7%, −16%, −25%, −27%; : 0%, 4%, 4%, 2%; : 11%, 24%, 37%, 48%; : −6%, −14%, −20%, −24%.) The posterior mean estimates of parameters are comparable using the other two priors.

When additional MRSA-colonized patients are admitted, and decline while and fluctuate. It suggests that patients with (HA- or CA-) MRSA colonization may have a lower risk of spreading MRSA in rural Alberta hospitals than patients with MRSA infections. In the meantime, also rises since it is anticipated that more unidentified MRSA patients would colonize susceptible people. The infection rate decreases when assuming that a small proportion of individuals are hospitalized with MRSA colonization.

Discussion

MRSA is a bacterium that can quickly spread among patients in acute care hospitals. Significant mortality rates in Canadian hospitals are caused by MRSA infections [7]. In this study, we focused on a stochastic compartmental model that can be used to simulate MRSA transmission in hospitals in multiple areas of Alberta. These areas include Calgary, Edmonton and rural Alberta, and they cover the entire province of Alberta.

When the model was fitted to data from all areas of Alberta, it predicted that for each contact with HA-MRSA-infected and CA-MRSA-infected patients, an average of 0.08 and 0.05 susceptible people would become new colonized patients each month. Each contact with HA-MRSA-colonized and CA-MRSA-colonized patients results in an average of 0.03 and 0.01 susceptible individuals becoming colonized per month, respectively. This indicates that infected patients spread the bacteria to more susceptible individuals than colonized patients. Patients with HA-MRSA colonization have an infection rate of 0.42. These results are similar to those from the analysis of the Edmonton hospital data.

Then, we assumed that certain individuals were colonized with MRSA upon admission [15] but were not promptly identified by medical staff. After a few days in the hospital, they were diagnosed with new HA-MRSA colonization. In Calgary hospitals, under the posterior mean estimates, HA-MRSA-colonized patients, HA-MRSA-infected patients, CA-MRSA-colonized patients, and CA-MRSA-infected patients colonize about 0.04, 0.5, 0.04, and 0.2 susceptible persons per contact per month, respectively, assuming 0.8 colonized patients per thousand admissions. The transmission rates appear to be marginally higher in Calgary than in Edmonton, but the credible intervals are relatively wide and overlapping which creates uncertainty in the interpretation. The marginal difference may be related to variations in infrastructure, such as the availability of multi-bed rooms. Patients in single-bed rooms may have easy access to hand rub dispensers, which are often located near the patient’s bed [33], and hand hygiene is the most effective strategy for controlling MRSA transmission in hospitals [34]. Transmission rates in rural areas seem to be lower than in Calgary but higher than in Edmonton, with their credible intervals overlapping. This uncertainty could be attributed to a variety of factors, such as the rural population’s smaller and more dispersed size, the hospitals’ patient mix, divergent practices, or a failure to detect colonized patients upon admission. We also performed an exploratory analysis combining data from Calgary hospitals and rural areas, and the results are consistent with using each dataset separately. Our findings also show that as the prevalence of unidentified colonized individuals rises in hospitals across Alberta, more susceptible individuals are colonized by infected patients than by colonized patients. As might be expected, more bacteria are shed by infected patients, or infected patients stay longer in hospitals and interact with others more frequently [35].

Our study does have limitations. In the model, there is some oversimplification of the MRSA transmission process. When healthcare personnel come into contact with MRSA patients, they may become contaminated and then colonize others who are susceptible. Bacteria in the environment may potentially affect transmission [13]. Because the prevalence rate of colonized cases upon admission is unknown, the inclusion of additional unobserved colonized patients upon admission may cause the model to exaggerate or underestimate real transmission rates in hospitals. Since we only have data from Alberta, data from other Canadian provinces are not included. We examine hospital data in each region of Alberta separately. The reason for this is that patient data is consolidated in multiple regions. As a result, the analysis excludes hospital transfers across regions, such as patients being transported between cities or rural areas, or being shifted from one city to another [36]. Furthermore, more people may be hospitalized during the respiratory season. Congested corridors in hospitals can lead to rapid MRSA transmission [37], but we did not find seasonal changes in the data.

Looking ahead, we could explore MRSA transmission patterns across different provinces employing the same analytical framework as our study. Notably, Ontario and several other regions report significant hospital-acquired MRSA infection rates [7]. Such a comparative analysis would illuminate transmission trends nationwide. At the same time, we ought to take into account additional elements that might influence the spread of MRSA within hospital settings, including examining the role of healthcare personnel who may carry MRSA or investigating how the presence of environmental bacteria affects transmission rates [13]. The model framework might be expanded by including compartments representing contaminated or uncontaminated HCWs and MRSA in the environment, such as medical equipment. MRSA in the environment has the potential to colonize patients and contaminate HCWs [13]. HCWs may also act as a vector for MRSA spread from colonized to uncolonized patients, especially through their contaminated hands [38]. Moreover, MRSA can spread rapidly among children and older adults, as these populations are particularly susceptible to infection [9]. Consequently, our model can be employed to analyze data that categorizes patients into various cohorts based on differing age demographics or gender proportions, enabling researchers to compare transmission rates across these distinct patient populations. Finally, the model could evaluate the efficacy of MRSA interventions across Alberta’s regions.

Conclusion

This study employed a Bayesian compartmental model to compare MRSA spread in Alberta hospitals and evaluate the impact of undetected colonized cases upon admission. The primary findings include that transmission rates appear to be marginally higher in Calgary than in Edmonton, which could be attributed to infrastructure variations such as multi-bed rooms. Rural locations seem to have lower transmission rates than Calgary but higher than Edmonton, which could be due to many factors such as population size and patient mix. Our modelling was consistent with infected patients having a higher propensity to transmit MRSA to susceptible individuals, possibly because they excrete more bacteria. These findings could help infection control specialists implement targeted interventions for MRSA patients in various hospitals to reduce MRSA transmission.

Abbreviation

MRSA

Methicillin-resistant Staphylococcus aureus

HA

Hospital-acquired

CA

Community-acquired

HCA

Healthcare-associated

HCW

Healthcare worker

MCMC

Markov chain Monte Carlo

CI

Credible interval

AHS

Alberta Health Services

IPC

Infection Prevention and Control

COVID

Coronavirus disease

Author contribution

RD, NL, JC and JL conceived the study. RL developed the methodology, conducted the formal analysis and wrote the original draft. RD and JL supervised, developed the methodology and acquired funding. All authors revised the manuscript and approved the final version.

Funding

This study was supported by Natural Sciences and Engineering Research Council of Canada (NSERC) Emerging Infectious Diseases Modelling (EIDM) Initiative, “Canadian Network for Modelling Infectious Disease (CANMOD)”.

Data availability

The data that support the findings of this study are available from Alberta Health Services but restrictions apply to the availability of these data, which were used under license for the current study, and so are not publicly available. Data are however available from the authors upon reasonable request and with permission of Alberta Health Services. The code for the simulation study can be found at https://github.com/RuoyL/unid_mrsa.

Declarations

Ethics approval and consent to participate

This study was conducted in accordance with the Declaration of Helsinki, and the protocol was approved by the Conjoint Health Research Ethics Board, University of Calgary (REB23-0934). Consent to participate is waived because the data are aggregated and anonymized, with no identifiable information.

Consent for publication

Not applicable.

Competing interests

The authors declare that they have no competing interests.