Identifying conditions for elimination and epidemic potential of methicillin-resistant Staphylococcus aureus in nursing homes
© The Author(s). 2016
Received: 8 February 2016
Accepted: 16 August 2016
Published: 22 September 2016
Residents of nursing homes are commonly colonized with methicillin-resistant Staphylococcus aureus (MRSA) but there is a limited understanding of the dynamics and determinants of spread in this setting. To address this gap, we sought to use mathematical modeling to assess the epidemic potential of MRSA in nursing homes and to determine conditions under which non-USA300 and USA300 MRSA could be eliminated or reduced in the facilities.
Model parameters were estimated from data generated during a longitudinal study of MRSA in 6 Wisconsin nursing homes. The data included subject colonization status with strain-specific MRSA collected every 3 months for up to 1 year. Deterministic and stochastic co-colonization and single-strain models were developed to describe strain-specific dynamics of MRSA in these facilities. Basic reproduction numbers of strain-independent MRSA, non-USA300 and USA300 MRSA were estimated numerically. The impact of antibiotic use in the past 3 months on the prevalence of strain-specific MRSA and associated basic reproduction numbers were evaluated.
Our models predicted that MRSA would persist in Wisconsin nursing homes, and non-USA300 would remain the dominant circulating strain. MRSA eradication was theoretically achievable by elimination of MRSA-positive admissions over the course of years. Substantial reductions in MRSA prevalence could be attained through marked increase in clearance rates or reduction in MRSA-positive admissions sustained over years. The basic reproduction number of strain-independent MRSA was 0.18 (95 % CI = 0.13–0.23). Recent antibiotic use increased the prevalence of strain-specific MRSA and associated basic reproduction numbers, but was unlikely to lead to an outbreak.
Based on our model, MRSA elimination from nursing homes, while theoretically possible, was unlikely to be achieved in practice. Decolonization therapy that can sustain higher clearance rates or lower MRSA-positive introductions over years may reduce strain-specific prevalence of MRSA in the facilities, and antibiotic stewardship may contribute to this effort. Large-scale MRSA outbreaks were unlikely in this setting.
KeywordsUSA300 MRSA Non-USA300 MRSA Colonization Nursing homes Epidemic potential Conditions for MRSA reduction
Methicillin-resistant Staphylococcus aureus (MRSA) is a major cause of healthcare- and community-associated infections . Infections caused by MRSA are more costly to treat and are associated with excess morbidity and mortality compared to infections caused by methicillin-sensitive strains of S. aureus [2, 3]. The dynamics of MRSA in hospitals has been explored in a number of studies [4–6] but its dynamics in other settings remains poorly understood. Up to 50 % of nursing home residents are colonized with MRSA [7–9] and these facilities may play an important role in regional spread of this pathogen [10, 11]. While mathematical models have previously been used to describe the role of nursing homes in the regional spread of MRSA [11–14], we are aware of only one study in which intra-facility dynamics of MRSA was modeled in nursing homes . In the latter study, mathematical modeling was used to explain the relative contribution of healthcare workers and residents to the spread of MRSA in nursing homes and the impact of some control strategies. Notably, model inputs employed in the latter study were based on data observed in a number of contexts, including non-nursing home settings.
Historically, specific strains – particularly, those designated by the USA100 CDC pulsotype – have been responsible for most of the MRSA observed in acute- and long-term care settings [7, 16]. However, an increasing number of studies suggest that community-associated strains of MRSA (e.g., USA300 MRSA) are becoming more common in healthcare facilities in the U.S. [16, 17]. This is of particular concern as community-associated strains may demonstrate a greater potential for transmission and virulence [18–20] that, when coupled with high levels of resident frailty, may produce more severe outcomes relative to healthcare-associated strains. Furthermore, a number of factors including recent antibiotic use have been implicated as risk factors for MRSA colonization in long-term care facilities [7, 8, 21]. However, their impact on the strain-specific dynamics of MRSA in nursing homes remains unexplained. Previously, we used Markov chain models to determine the ultimate distribution of residents colonized with non-USA300 and USA300 and to assess the influence of MRSA strain-type and potential risk factors on MRSA acquisition in nursing homes . We found that non-USA300 strains would remain dominant in nursing homes. Among the candidate risk factors considered in our study, antibiotic use within the past 3 months was the only one to significantly increase the acquisition rates of strain-independent and non-USA300 MRSA.
The transmission dynamics of non-USA300 and USA300 MRSA in nursing homes remains largely unexplained. For instance, while nursing homes are known as reservoirs of MRSA , the risk of MRSA outbreak and the prospects of MRSA reduction or elimination in this setting have not been well-understood. Furthermore, the effect of resident-specific characteristics, such as previous antibiotic use, and facility-specific characteristics, such as admission and discharge of colonized, on epidemic potential of MRSA have not been established. In this work, we focused on studying the epidemic potential of MRSA and the relative merits of interventions to reduce or eliminate MRSA from nursing home facilities using compartmental and stochastic modeling approaches. It should be noted that we focused on the U.S. nursing homes most of which provide a mixture of post-acute, rehabilitative and domiciliary services to residents that are generally elderly and require ongoing skilled nursing care. The specific aims of this study were: (1) to evaluate the impact of selected measures on the prevalence of strain-specific MRSA over time and to determine the conditions for MRSA elimination from study nursing homes; (2) to assess the epidemic potential of MRSA and its sensitivity to changes in acquisition and clearance rates, and admission and discharge of colonized; (3) to assess the impact of antibiotic use in the previous 3 months on the prevalence of strain-specific MRSA and its outbreak potential.
Deterministic compartmental models were developed to describe the transmission dynamics of MRSA in the study nursing homes. Stochastic models were subsequently simulated to assess the impact of randomness on predicted outcomes. The study was reviewed and approved by the Health Sciences Institutional Review Board of the University of Wisconsin-Madison.
All model inputs, including model parameters, were derived from data collected during a longitudinal study of antibiotic resistance in six nursing homes in Wisconsin . MRSA surveillance cultures were collected from multiple anatomical locations of each subject at baseline and every 3 months thereafter for a period of up to 1 year . The subject’s MRSA status was considered non-evaluable if a culture from any of the routinely screened body sites was missing. Thus, 446 out of 449 subjects contributed evaluable observations to this study. It should be noted that the baseline assessment was not evaluable for two subjects with multiple observations over the study period . Their assessment at 3 months was considered as baseline assessment for the purpose of this study. Data on antibiotic use in the previous 3 months, dichotomized into No or Yes, were abstracted from health records at the time surveillance cultures were performed. Most of the antibiotics were administered orally and were prescribed for treating urinary tract infection. About 15 % of antibiotics, including sulfonamides and tetracyclines, may have possessed anti-MRSA activity. The data from the six study nursing homes were merged to improve the precision of results; that is, the study outcomes are representative of the hypothetical “combined” Wisconsin nursing home. Facility-level differences in characteristics of these nursing homes and MRSA colonization trends in individual facilities were described elsewhere [22, 23].
The co-colonization model in a deterministic framework was used to assess the relative merits of selected interventions, the outbreak potential of MRSA, and the impact of antibiotic use in the past 3 months on MRSA prevalence and a possibility of outbreak. To evaluate the relative contribution of each strain-type to the outbreak potential of MRSA, single-strain models in a deterministic framework were also considered (Fig. 1b).
In all models, the number of contacts between residents was assumed to be independent of the size of the nursing home (this assumption regarding the underlying structure of contacts is referred to as frequency-dependent transmission or mass action ). Colonization was assumed to occur via random mixing between colonized and non-colonized residents. No distinction was made between colonized and infected. The entire dataset was used to implement every model. The computation was performed in R, version 3.1.0 and higher .
Transmission dynamics of MRSA and impact of selected measures on its prevalence over time
Parameters and initial occupancy for the co-colonization model
Value (95 % CI)
Estimated or Observed
Initial occupancy in each compartment
Number of residents susceptible to any MRSA
Number of residents colonized with non-USA300
Number of residents colonized with USA300
Number of residents co-colonized with non-USA300 and USA300
Total number of residents
Probability of admission of MRSA-colonized residents
Discharge rate of susceptibles (per 3 months)
Discharge rate of MRSA-colonized (per 3 months)
Proportion of residents colonized with non-USA300 at baseline
Proportion of residents colonized with USA300 at baseline
Proportion of residents co-colonized with both strains at baseline
Acquisition rate for non-USA300a
0.029 (0.022, 0.038)
- w/o ABc
0.020 (0.014, 0.030)
- with ABd
0.042 (0.030, 0.061)
Acquisition rate for USA300a
0.006 (0.004, 0.011)
- w/o ABc
0.004 (0.002, 0.010)
- with ABd
0.009 (0.005, 0.019)
Clearance rate for non-USA300a
0.116 (0.088, 0.152)
- w/o ABc
0.125 (0.086, 0.179)
- with ABd
0.107 (0.074, 0.163)
Clearance rate for USA300a
0.137 (0.082, 0.228)
- w/o ABc
0.155 (0.079, 0.328)
- with ABd
0.125 (0.064, 0.266)
The stability of endemic and disease-free equilibria  (the state of the system when no changes are observed over time, while the disease is present or absent, respectively) was established by dynamically running the system of differential Eqs. (1) with the initial conditions (Table 1) to steady-state using the rootSolve package in R environment . The steady-state tolerance was set to the nearest hundredth.
The sensitivity analysis of the MRSA prevalence to the estimated parameters of the model was performed. The changes in the point prevalence of non-USA300 and USA300 MRSA over time were predicted for the values of admission prevalence, (λ) between 0 and 0.5 with step 0.1. This range includes and exceeds the admission prevalence of MRSA reported in other studies [9, 15, 16]. The ranges for the sensitivity analysis of discharge rates of colonized and non-colonized (γI and γS) were chosen based on the respective interquartile ranges of resident length of stay across the facilities. Thus, discharge rates of 0.05-1.05 (step 0.2) for colonized and 0.05-0.55 (step 0.1) for non-colonized were employed in the sensitivity analysis. Acquisition rates (b 1n and b 3n ) up to three times as high as the estimate for non-USA300 and 10 times higher than the estimated rate for USA300 were considered for the sensitivity analysis (that is, 0–0.12 (step 0.02) for non-USA300 and 0–0.06 (step 0.01) for USA300). Clearance rates (g n1 and g n3 ) between the values twice lower and twice higher than estimated rates were employed in the sensitivity analysis (that is, 0.058–0.232 (step 0.029) for non-USA300 and 0.068–0.278 (step 0.042) for USA300).
Scenario 1: elimination of intra-facility MRSA cross-transmission (b 1n = b 3n = 0; Table 1),
Scenario 2: doubling of the strain-specific MRSA clearance rates (2×[g n1 ] and 2×[g n3 ]; Table 1),
Scenario 3: elimination of all MRSA-positive admissions (λ = 0; Table 1),
Scenario 4: elimination of a half of MRSA-positive admissions (λ/2; Table 1).
Elimination of intra-facility cross-transmission (Scenario 1) could theoretically be achieved through active surveillance and adherence to more aggressive forms of contact precautions than the ones commonly employed in nursing homes or decolonization therapy [28, 29]. It should be noted that by cross-transmission we understood transition from being non-colonized to colonized with non-USA300 or USA300 strain of MRSA, or transition from colonized with non-USA300 or USA300 to co-colonized with both strains. Decolonization therapy was shown to increase MRSA clearance rates (Scenario 2) in nursing homes . Elimination or reduction in MRSA-positive admissions (Scenarios 3 and 4) could be achieved through active surveillance at admission coupled with decolonization therapy . This intervention was implemented by some hospitals, and positive results were reported [30, 31]. Furthermore, reducing MRSA prevalence and transmission in the community and healthcare settings that transfer patients to nursing homes, including acute-care hospitals, may reduce the admission prevalence of MRSA in nursing home facilities. The prevalence of MRSA under each scenario may help to inform infection control in nursing homes.
The stochastic co-colonization model was a continuous-time Markov chain model and was simulated using Gillspie’s algorithm [32, 33]. The possible state transitions of the model and their respective rates are presented in Appendix Table A1. The model was simulated 1000 times, and the mean of the 1000 simulations was calculated.
Assessing epidemic potential of MRSA
The basic reproduction number, R0, was used as a threshold to assess the epidemic potential of MRSA in the study nursing homes. In the context of our study, R0 represented the expected number of secondary cases of colonization with strain-independent MRSA caused by a single MRSA-colonized resident in a totally susceptible population . A value of R0 greater than 1 would predict the spread of MRSA in the population over time and imply that MRSA may become epidemic. The basic reproduction number was estimated by the Next Generation Method , using pertinent parameters from Table 1. Standard errors and 95 % confidence intervals (CI) around point estimates were computed by means of bootstrapping with 1000 resampling runs and assuming approximate normality of standard errors .
For the co-colonization model (Fig. 1a), the basic reproduction number was examined over the space of acquisition and clearance rates of non-USA300 and USA300 within their 95 % CI’s (Table 1). For that purpose, the 95 % CI’s for the four rates (Table 1) were partitioned into steps of size 0.001, and an R0 was recalculated for each possible combination of the rates. Furthermore, the sensitivity of R0 to the acquisition and clearance rates, discharge rate of colonized, and probability of MRSA-positive admissions was assessed in a one-way sensitivity analysis in which each parameter was varied between 0 and 1 while keeping all other model parameters at their fixed values.
Impact of antibiotic use in the previous 3 months
The co-colonization model (Fig. 1a) with antibiotic-specific acquisition and clearance rates (Table 1) was used to estimate the changes in the point prevalence of strain-specific MRSA over time for each level of recent antibiotic use (Yes and No). The hypothetical “best case” and “worst case” scenarios were examined by using the combinations of upper and lower bounds of the 95 % CI’s around antibiotic-specific acquisition and clearance rates (Table 1). The “worst case” scenarios assumed high acquisition and low clearance, while the “best case” scenarios were low acquisition and high clearance. For each level of antibiotic use, the basic reproduction numbers R0, R01 and R03 were estimated from the co-colonization model (Fig. 1a) and respective single-strain models (Fig. 1b) in which antibiotic-specific acquisition and clearance rates were used (Table 1).
Elimination of intra-facility cross-transmission had a modest impact on the predicted prevalence of non-USA300 and very little impact on the predicted prevalence of USA300 and co-colonized with both strains (Scenario 1 in Fig. 2). Greater reductions in the prevalence of MRSA could be achieved through doubling clearance rates or reducing the probability of admission of colonized two-fold (Scenarios 2 and 4 in Fig. 2). The only scenarios under which MRSA extinction could be achieved were through elimination of all MRSA-positive admissions (Scenario 3 in Fig. 2) or through selective discharge of colonized residents (Appendix Figure A4). It should be noted, however, that predicted reductions or elimination of MRSA would take years even if any of these unlikely conditions could be achieved.
Basic reproduction number for strain-independent and strain-specific MRSA
Basic Reproduction Number
Point Estimate (95 % CI)
General (irrespective of AB)
Strain-independent MRSA, R0
0.18 (0.13, 0.23)
0.12 (0.07, 0.17)
0.28 (0.16, 0.40)
0.16 (0.11, 0.21)
0.11 (0.06, 0.15)
0.24 (0.15, 0.34)
0.04 (0.01, 0.06)
0.02 (0.00, 0.05)
0.05 (0.02, 0.09)
Residents of nursing homes are commonly colonized with MRSA and there is increasing recognition that these facilities influence patterns of MRSA within other healthcare facilities in the same region [36, 37]. Mathematical modeling has been extensively used to understand the dynamics of MRSA within hospitals and its spread between healthcare facilities within the same region [4, 6, 12, 13]. In contrast, attempts to employ mathematical modeling to gain a better understanding of the dynamics of MRSA within the nursing home context remain sparse. The current study advances our knowledge about the prospects of reducing or eliminating MRSA from nursing homes and, conversely, the potential for these facilities to experience a MRSA outbreak. It also examines the impact of recent antibiotic use on the prevalence of MRSA and its outbreak potential.
Our study suggests that elimination of MRSA from nursing homes in the U.S. is highly unlikely under any reasonable conditions. Based on our model, eradication of MRSA could be eventually achieved in nursing facilities if all MRSA-positive admissions were eliminated over a prolonged period of time (years). This intuitive finding is similar to the finding of the other modeling study , which concluded that MRSA would persist in nursing homes for as long as colonized residents continue to enter the facilities. Elimination of MRSA introductions could theoretically be achieved through active surveillance, particularly when coupled with effective social distancing interventions or decolonization therapy. Nevertheless, the likelihood of achieving these outcomes in actual practice seems remote for a variety of reasons.
Surprisingly, elimination of intra-facility cross-transmission had a minimal impact on the predicted prevalence of strain-specific MRSA over years. While acquisition rates depend on the intrinsic characteristics of the pathogen, they may also be influenced by colonization pressure  and mixing patterns among residents and between residents and staff within the facilities. Several studies have demonstrated that active surveillance, particularly when combined with social distancing measures, can be effective in reducing MRSA prevalence in hospitals and nursing homes [29, 39]. However, the findings of our study suggest that this approach would be of limited utility in nursing homes. This is particularly germane in the long-term care setting where social interactions between residents are considered a goal of care.
Two-fold increase in strain-specific clearance rates or two-fold decrease in MRSA-positive admissions, which could be achieved through the use of decolonization therapy , was associated with more substantial reductions in strain-specific prevalence of MRSA if sustained for several years. However, limitations in currently available de-colonization interventions may be a significant barrier to this reduction approach. Intra-nasal mupirocin has been shown to reduce (but not to eliminate) MRSA carriage in several nursing home studies [28, 41]. Coupled with imperfect surveillance for MRSA [7, 42, 43], these reductions may be more moderate than expected. Moreover, these studies demonstrated that de-colonization in most residents was transient and associated with the emergence of resistance . Consequently, the effectiveness of using mupirocin to reduce the prevalence of MRSA in nursing homes over the long run may be limited.
Taken together, our findings suggest that MRSA elimination in nursing homes is unlikely but reductions in the prevalence of MRSA are theoretically achievable, particularly through interventions that accelerate the rate of resident de-colonization or reduce the admission prevalence of MRSA. Nevertheless, our models predict that these interventions would need to be sustained over a period of years in order to have a demonstrable effect on observed patterns of colonization.
An MRSA outbreak in the study nursing homes as quantified by an R0 value greater than 1, while theoretically possible, was only achievable under extraordinary circumstances (e.g., multi-fold increase in MRSA acquisition rates). However, minor strain-specific outbreaks were observed during a number of realizations of the stochastic model. Collectively, these findings suggest that while major MRSA outbreaks are unlikely to take place in nursing homes, minor outbreaks may occasionally occur. The basic reproduction number of non-USA300 appeared to be significantly higher than that of USA300 suggesting a higher epidemic potential of non-USA300 strain of MRSA. Furthermore, while recent antibiotic exposure elevated epidemic potential of MRSA, it was unlikely to lead to an outbreak. More research is needed to study factors that may lead to MRSA outbreaks in nursing homes and to evaluate possible outbreak prevention strategies.
The limitations of our study are primarily influenced by the scarcity of data, particularly for USA300 MRSA, and modeling assumptions. For example, while individual nursing homes may differ in transmission dynamics of MRSA, we combined the data from the six facilities due to its paucity in individual facilities. Hence, the results would be applicable to a hypothetical “combined” nursing home. On the other hand, in our previous work we found that the patterns of predicted prevalence at steady state in most facilities mirrored the patterns for pooled data .
The standard assumption of random mixing among residents may not be realistic in nursing homes where residents tend to socialize selectively, may share a room, may have limited mobility or be bed-bound. Even though our homogeneous-mixing model predicted that MRSA outbreaks were unlikely in the study nursing homes, they may actually be occurring in subgroups of residents (e.g., in subgroups with substantially higher contact rates between colonized and susceptibles). Our simplifying assumption of constant acquisition and clearance rates of strain-specific MRSA may not be true in nursing homes. The reasons include the variability in contact patterns among residents and between residents and staff, differences in exposure to potential risk factors, colonization pressure  and the effect of super-spreaders . Furthermore, we assumed that transmission and acquisition of either strain was independent of colonization status with the other strain, while there is no evidence in favor or against this assumption. Moreover, our models did not account for MRSA transmission through hands of health care workers which may play a role in the spread of MRSA in nursing homes [15, 45]. Additionally, the admission prevalence of MRSA that was assumed to be constant in our models may vary over time. The reasons include differences in the prevalence of MRSA colonization among residents admitted from hospitals and the community.
A number of model parameters were not readily available in our dataset and were estimated from our data. Thus, the point prevalence of MRSA at baseline was used as admission prevalence, though these values may differ in practice. One study of ten nursing homes in California found that the point prevalence of MRSA, while being significantly higher, correlated well with the admission prevalence in the study facilities . MRSA admission prevalence reported in this study varied between 8 % and 31 %, with half of the facilities admitting 21 % or more of MRSA colonized . Our estimate of 0.215 is comparable with MRSA admission prevalence reported in that study, but is higher than those in other studies [15, 16]. It is also likely to be an overestimate for our study facilities. If so, our results may be a worse prognosis than reality. On the other hand, if the length of stay for non-colonized is lower than our estimate, then our prognosis may be too optimistic. Based on our sensitivity analysis, realistic changes in other estimated parameters are unlikely to substantially alter the predicted prevalence. Given a limited knowledge of MRSA patterns in nursing homes, our study is an important step in continuum research that aims at improving our understanding of the dynamics of strain-specific MRSA in nursing homes.
To our knowledge, our study is the first modeling study that sought to assess the epidemic potential of strain-specific MRSA, to evaluate the conditions for MRSA elimination, and to examine the relative merits of selected reduction scenarios of stain-specific MRSA in nursing homes. More research is needed to assess other potential conditions for reducing MRSA colonization in nursing homes and evaluate their cost-effectiveness. Modeling techniques that accommodate heterogeneity of mixing patterns among residents may be a valuable tool in this effort. Furthermore, examining the associations between the candidate risk factors for MRSA colonization and MRSA pulsotypes differentiated at a higher strain similarity threshold may aid in better informing the choice of interventions aimed at reducing the burden of MRSA in nursing homes in the U.S.
We used mathematical modeling to assess the outbreak potential of MRSA colonization in nursing homes and to evaluate conditions for eliminating or reducing MRSA in this setting. Our study suggests that despite the presence of USA300 strains in a number of the study nursing homes, non-USA300 will remain the dominant circulating MRSA strain in Wisconsin facilities. We found that MRSA elimination from the U.S. nursing homes, while theoretically possible, is unlikely to be achieved in practice. Marked reductions in the strain-specific MRSA in this setting may be attained by using active surveillance coupled with decolonization therapy that can sustain substantially higher clearance rates or reductions in MRSA admission prevalence over years, and antibiotic stewardship may contribute to this effort. Eliminating intra-facility cross-transmission had little impact on the predicted prevalence of MRSA in our models. Despite the recent emergence of novel MRSA strains, including USA300, our models predicted that large-scale outbreaks were unlikely in the nursing home setting.
Methicillin-resistant Staphylococcus aureus
We would like to express our great appreciation to Drs. Vicki Bier, Molly Carnes and David Zimmerman for their constructive suggestions, invaluable feedback, and support during different stages of the study. We would like to thank Ms. Helena Tsotsis for her help with data retrieval.
Christopher J. Crnich activity on this project was supported by the Clinical and Translational Science Award (CTSA) program, through the NIH National Center for Advancing Translational Sciences (NCATS) (Grant UL1TR000427; the content is solely the responsibility of the authors and does not necessarily represent the official views of the NIH); the University of Wisconsin School of Medicine and Public Health, through the Wisconsin Partnership Program; and a research scholarship from the ASP/IDSA T. Franklin Williams Program.. David F. Anderson was supported through NSF grants DMS-1009275 and DMS-1318832 and Army Research Office grant W911NF-14-1-0401.
Availability of data and materials
The dataset supporting the conclusions of this article is available in the [repository name will be provided] repository [unique persistent identifier and hyperlink to dataset(s) in http:// format will be provided].
NGB contributed to the conception and design of the study, performed mathematical modeling, interpreted the results, and wrote the manuscript. CJC provided the data for this study, contributed to the conception and design of the study, interpretation of the results and their implications to the field, and oversaw the revision of the manuscript. DFA contributed to the design of the study, developing and implementing mathematical models, interpreting the results, and revising the manuscript. DD conceived and designed the study, and supervised mathematical modeling, interpretation of the results and writing the manuscript. All authors reviewed the manuscript and approved the final version of the manuscript for publication.
The authors declare that they have no competing interests.
Consent for publication
Ethics approval and consent to participate
The study was reviewed and approved by the Health Sciences Institutional Review Board of the University of Wisconsin-Madison.
Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated.
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