ABSTRACT
Staphylococcus aureus is a major pathogen causing intramammary infections (IMI) in dairy cattle herds worldwide. Simulation models can be used to investigate the epidemiologic and economic outcomes of different control strategies against IMI. The transmission rate parameter is one of the most influential parameters on the outcomes of these simulation models. Very few studies have estimated the transmission rate parameter and investigated the transmission dynamics of Staph. aureus IMI in dairy cattle herds. The objective of our study was therefore to analyze the transmission dynamics of Staph. aureus in 2 Danish dairy herds participating in a longitudinal study. The 2 herds had 180 and 360 milking cows, and animals were tested at quarter level once per month over a period of 1 yr. We estimated the quarterlevel prevalence to be 34% for herd 1 and 2.57% for herd 2. The daily quarterlevel transmission rate was estimated to be 0.0132 and 0.0077 cases/quarterday for herds 1 and 2, respectively, and the median duration of infection was estimated to be 91 and 64 d for herds 1 and 2, respectively. We also estimated the reproductive ratio at 1.21 for herd 1 and 0.52 for herd 2. The results can provide valuable information for simulation models to aid decisionmaking in terms of the prevention and control of Staph. aureus IMI in dairy cattle herds.
Key words
INTRODUCTION
Mastitis is one of the most widespread and costly diseases in dairy herds worldwide (
Halasa et al., 2007
; Schwarz et al., 2010
). Cows with mastitis or IMI can have an increased SCC, decreased milk quality, and impaired performance. If cows develop clinical signs, they must be treated or culled and the milk must be discarded, with milk loss potentially continuing even after recovery (Gröhn et al., 2004
; Hertl et al., 2014
).To prevent the spread of pathogens among cows, control of contagious IMI pathogens in dairy herds requires consistent management actions such as postmilking teat dipping, antibiotic treatment, and culling of infected animals (
Hillerton et al., 1995
). These management strategies can be simulated in prediction models to investigate the epidemiological and economic effects of the actions against IMI (Lam et al., 1996
; Seegers et al., 2003
; van den Borne et al., 2010
; Halasa, 2012
; Gussmann et al., 2018
). The spread of pathogens can be simulated based on knowledge of the transmission dynamics in a herd (Kirkeby et al., 2017
).Contagious pathogens that cause IMI (such as Staphylococcus aureus) are believed to be transmitted between lactating cows primarily through milking equipment (
Harmon, 1994
). When modeling the spread of Staph. aureus, the transmission rate, number of infectious animals, and total number of lactating cows can be used to estimate the probability of infection (Halasa et al., 2009
). The number of new IMI cases is therefore highly dependent on the transmission rate, which can have a considerable influence on the model predictions (Halasa et al., 2009
; Down et al., 2013
). Furthermore, variation in the estimated transmission rates may affect the costeffectiveness of simulated control actions. In addition, it is important to estimate the transmission rate under different levels of prevalence to investigate the epidemiological effect and costeffectiveness of control measures at these levels. A measure that might be costeffective at a high prevalence level might not be cost effective at a low level simply because the infectious pressure would be different.Transmission rates can be estimated from longitudinal studies, in which a population of lactating cows is followed over time and samples are collected and tested regularly (e.g.,
Lam et al., 1996
; Zadoks et al., 2001a
; Barlow et al., 2013
; Leelahapongsathon et al., 2016
). The more sampling points (time points for sampling) available, the more precisely the transmission rate can be estimated. However, such longitudinal studies are costly and difficult to undertake, which is why few studies have been conducted. To the best of our knowledge, only 5 studies have estimated the transmission rate of Staph. aureus within dairy cattle herds (Lam et al., 1996
; Zadoks et al., 2002
; Barlow et al., 2013
; Schukken et al., 2014
; van den Borne et al., 2017
). Such studies are needed to minimize the uncertainty of predictions of simulation models.The objective of our study was to investigate the transmission dynamics of Staph. aureus in 2 Danish dairy herds—one with low prevalence and one with high prevalence—from a longitudinal study over 1 yr using monthly sampling intervals. Furthermore, the duration of infection and the basic reproductive ratio (R_{0}) for Staph. aureus were estimated and compared for the 2 studied herds.
MATERIALS AND METHODS
Animals and Farms
Milk samples were collected every month between January 2017 and January 2018 from 2 conventional dairy herds with sidebyside milking parlors located in the central region of Jutland, Denmark (Table 1, Table 2). This sampling interval was chosen as a compromise between sampling often enough to detect new infections before a possible recovery (allowing for estimation of transmission rate and duration of infection), covering all seasons to investigate the transmission throughout the year, and keeping a reasonable budget. The average herd size in Denmark is 180 lactating cows, and this number is continually increasing. Our study herds comprised approximately 180 and 360 lactating cows. We considered herds at least with 180 cows to reflect the general herd size in Denmark and selected a herd with minor Staph. aureus problems and a herd with considerable Staph. aureus problems. In addition, the farmers agreed to participate in the study without changing their routines or management throughout the whole sampling period. Furthermore, we intended to include herds with different levels of IMI problems to estimate transmission under good and bad situations. This allowed the transmission rate at 2 different levels of IMI problems to be quantified. The included herds are further described below. Before sampling, the functionality of the milking systems was controlled through technical measurements according to ISO standards 3918, 5707, and 6690 (
ISO. (International Organization for Standardization), 2007a
,ISO. (International Organization for Standardization), 2007b
,ISO. (International Organization for Standardization), 2007c
).Table 1Descriptions of herd 1 and herd 2 in the 12mo sampling period
Item  Herd 1  Herd 2 

Breed  Holstein  Holstein 
Number of milked cows  180  360 
Housing  Freestall  Freestall 
Number of housing groups for lactating cows  2  1 
Bedding material  Straw  Sand 
Calving box material  Straw boxes (deep bedded packs)  Straw boxes (deep bedded packs) 
Dryoff box material  Straw boxes  Straw boxes 
Feed  TMR mix of soy, barley, concentrated feed, corn, and grass silage  TMR mix of soy, concentrated feed, and corn silage 
Average daily milk yield per cow (kg)  27.4  36.7 
Bulk milk SCC in the study period (cells/mL)  294,000 (range: 261,000–324,000)  280,000 (range: 236,000–299,000) 
Milking system  Sidebyside, 12 × 2  Sidebyside, 16 × 2 
Milking interval  2 times a day  3 times a day 
Total number of quarter samples collected  8,560  17,372 
1 Average daily milk yield per cow based on the last 25 monthly milk yield controls and the average herd size during the study.
Table 2Sampling dates, length of sampling intervals, number of quarter samples, and number of cows sampled in the study
Date  Interval  No. of cows  No. of cows with single quarter infections  No. of cows with multiple quarter infections 

Herd 1  
16.01.2017  —  180  45  57 
13.02.2017  28  181  52  62 
14.03.2017  29  175  45  73 
10.04.2017  27  177  48  74 
08.05.2017  28  169  42  71 
12.06.2017  35  179  39  70 
10.07.2017  28  180  42  49 
14.08.2017  35  178  56  49 
11.09.2017  28  178  42  46 
09.10.2017  28  174  42  62 
13.11.2017  35  183  45  65 
11.12.2017  28  181  48  64 
Herd 2  
06.02.2017  —  347  29  5 
06.03.2017  28  358  27  6 
03.04.2017  28  360  25  8 
01.05.2017  28  360  26  7 
06.06.2017  36  344  33  6 
03.07.2017  27  334  20  3 
07.08.2017  35  354  12  3 
04.09.2017  28  359  15  2 
02.10.2017  28  364  12  1 
06.11.2017  35  371  10  2 
04.12.2017  28  396  17  4 
08.01.2017  35  392  23  9 
Herd 1
Herd 1 comprised 180 (174–183) lactating cows, as well as dry cows, heifers, and calves (Table 1). Cows were milked twice per day and no animals were purchased during the study period. The milking system was a double 12 sidebyside milking parlor. Primiparous animals were milked in one side of the milking parlor and older animals were milked in the other side. At milking, the teats were wiped off with clean cotton rags. One rag per cow was used and they were soaked in hot water before use. Postmilking teat dipping was performed in this herd. Cows were tested with bacterial culture at dry off if their SCC was above 200,000; if positive, cows treated with intramammary antibiotics and teat sealant. Clinical mastitis cases during the lactation were treated with antibiotics and nonsteroidal antiinflammatory drugs. If the treatment did not work, clinically ill cows were culled.
The bedding material in the freestalls was straw and the feed was a TMR consisting of soy, barley, concentrate, corn, and grass silage. From March to August 2017, a problem with mycotoxins in the feed occurred, and from July on the animals were given an antidote. From August 20, 2017, all silage used on the farm was replaced with a new silage product to avoid toxins in the feed. During the study period, herd 1 had a mean bulk milk SCC of 294,000 (range = 261,000–324,000 cells/mL).
Herd 2
Herd 2 comprised 360 (334–396) lactating cows, as well as dry cows, heifers, and calves (Table 1). The milking system was a double 16 sidebyside milking parlor and sand was used as bedding material. Milking personnel used gloves and the teats were wiped off with clean rags (one per cow); postmilking teat dipping was not performed. Cows were treated with intramammary antibiotics and teat sealant if positive by bacterial culture at dry off. Clinical infections during lactation were treated with antibiotics and nonsteroidal antiinflammatory drugs. If this treatment did not work, the clinically ill cow was culled. Cows were milked 3 times per day and the feed was a TMR mix of soy, concentrate, and corn silage. This herd was closed until midNovember 2017, when 30 animals were purchased from another farm. These animals were included in sampling from December 4, 2017. During the study period, herd 2 had a mean bulk milk SCC of 280,000 (range = 236,000–299,000 cells/mL).
Collection of Quarter Milk Samples
Quarter foremilk samples were collected in accordance with NMC standards (http://www.nmconline.org/sampling.htm). Specifically, a premilking teat preparation product was used to dissolve dirt and thereby ensure proper cleaning of the quarters. In herd 1, a foaming teat wipeoff product (Viri Foam,Novadan ApS, Kolding, Denmark) was sprayed onto the teats. In herd 2, teats were predipped using milk wash from Trinol (Hobro, Denmark). Teats were then cleaned with cotton towels soaked in water and a minimum of 4 squirts of milk were discarded from each quarter. The teats were then sanitized using singleservice wet wipes (MS Lavettes, MS Schipper, Bladel, the Netherlands) soaked in 90% ethanol, using one towel per teat. Cleaning started with teats on the far side of the udder. Teat ends were cleaned until no more dirt appeared on the wipe. The teats were then sprayed with 90% ethanol and left to air dry for a minimum of 30 s before sampling. Prelabeled sterile sample vials were used for sampling (Sarstedt, 62.554.002, 15 mL, 120 × 17 mm sterile tubes, Nümbrecht, Germany). The sample vial was filled with up to 15 mL of milk and immediately recapped. Sampling started at the nearest teat and progressed to the teats on the far side of the udder. Samples were stored in thermally insulated boxes with cooling elements for shipment to the laboratory and were processed within 36 h of sample collection. Samples were preserved with 0.5% boric acid (
Heeschen et al., 1969
; International Dairy Federation, 1981
) and shipped to another laboratory in thermally insulated boxes with cooling elements for bacteriological analysis and processed within 48 h of collection.Laboratory Analysis
Culture and identification of isolates were performed at Landesbetrieb Hessisches Landeslabor (LHL), Gießen, Germany, according to the DVG (
German Veterinary Association, 2009
) guidelines for the isolation and identification of IMIcausing pathogens. The DVG guidelines are based on recommendations given by Hogan et al., 1999
and Pedersen et al., 1981
. A sterile glass loop was used to streak 10 µL of each milk sample per quarter of a plate (1 plate per cow). Milk samples were cultured on cattle blood agar containing 0.1% esculine (CBA; Oxoid, Wesel, Germany) at 37°C under aerobic conditions for up to 48 h. Plates were read after 24 and 48 h. If a minimum of 1 colony was present in the sample, it was identified as positive. Phenotypic characterization was performed by standard microbiological procedures on single representative colonies of each morphologically distinct isolate. Hemolytic properties and esculine degradation properties of the bacteria were examined on CBA. Microscopic examinations of fixed smears of the isolates were performed using Gram stain. Gram staining was done according to the Hucker method, as described previously (Gerhardt et al., 1994
). Cell morphological features were observed under a Leitz Diaplan light microscope at ×1,000, with cells grown for at least 18 h at 37°C on CBA. Bacterial colonies were tested for catalase activity with 3% H_{2}O_{2} on microscopic slides and for presence of cytochrome oxidase with the BBL DrySlide Oxidase system (Becton Dickinson, Heidelberg, Germany). As Streptococcus agalactiae displays a regular Christie, Atkins, MunchPetersen (CAMP) phenomenon (Hensler et al., 2008
) when tested with an orthogonally growing Staph. aureus (ATCC 25923, American Type Culture Collection; Manassas, VA), this test was routinely carried out. Presumptive identification of streptococci was based on the aforementioned criteria as well as on confirmation with Lancefield group antigenspecific Streptococcus antisera (Phadebact, MKL Diagnostics AB, Sollentuna, Sweden). Final confirmation of presumptive identification was done by MALDITOF (Barreiro et al., 2010
). Bacterial isolates representing putative mastitis pathogens as well as concomitant bacterial microbiota were selected from the culture plates and then directly transferred to steel targets according to the manufacturer's instructions (BrukerBiotyper,  Barreiro J.R.
 Ferreira C.R.
 Sanvido G.B.
 Kostrzewa M.
 Maier T.
 Wegemann B.
 Böttcher W.
 Eberlin M.N.
 Dos Santos M.V.
Identification of subclinical cow mastitis pathogens in milk by matrixassisted laser desorption/ionization timeofflight mass spectrometry.
J. Dairy Sci. 2010; 93 (21094737): 56615667
Bruker Daltonik, 2012
). Isolates were prepared using the direct smear method and analyzed on a Bruker Microflex LT system by MALDITOF MS using Biotyper Version V3.3.1.0 (DB 5989, Bruker Daltonik, 2012
). The MALDI Biotyper realtime classification software considers MALDI scores >2.3 and >2.0 as secure species and genus identification levels, respectively. Colonyforming units per milliliter measures were not obtained. Plates were defined as contaminated if 4 or more phenotypically different bacterial species were found.Statistical Analysis
Data Management
Analyses were carried out in R 3.5.1 “Feather spray” (
R Core Team, 2018
). We obtained data from the Danish cattle database on the dates of drying off for each cow during the study period. Quarterlevel prevalence was calculated per sampling day based on the bacterial culture result. Cowlevel prevalence was calculated on the basis that a cow was infected if one of its quarters was positive. A quarter with a positive Staph. aureus result that followed a negative result was considered to be a new IMI case. Cows that had a negative result at the dry off sample and a positive one in the first sample after calving were also considered new IMI cases.The following assumptions were used to correct missing data points. A missing value between 2 positive samples was considered positive; a missing value between 2 negative samples was considered negative; and, for simplicity, missing values between any negative and positive samples were considered negative. In addition, if a quarter had a negative test between 2 positive samples, we corrected it to positive assuming a falsenegative result due to imperfect test sensitivity (e.g.,
Mahmmod et al., 2013
) or the potential intermittent shedding pattern known for Staph. aureus ( Mahmmod Y.S.
 Toft N.
 Katholm J.
 Grønbæk C.
 Klaas I.C.
Bayesian estimation of test characteristics of realtime PCR, bacteriological culture and California mastitis test for diagnosis of intramammary infections with Staphylococcus aureus in dairy cattle at routine milk recordings.
Prev. Vet. Med. 2013; 112 (23992955): 309317
Sears et al., 1990
). Infections were regarded as cured when a negative test result occurred after a positive test and no positive test followed after that. We did not consider that heifers could be infected before introduction to the herd; thus, all infections that were observed were regarded as new infections unless the animal had previously been positive. The cured animals in this analysis comprise both spontaneously cured animals and treated animals. No animals were treated due to subclinical mastitis, but all clinically infected animals were treated with antibiotics for 3 d. For this reason, we were not able to separate the flareup rate (from subclinical to clinical) from the spontaneously cured animals. For each sampling point, we calculated the number of transient infections. Transient infections were defined as positive test results that were preceded and followed by a negative result. We also calculated the number of new infections in quarters on cows that did not have a previous Staph. aureus infection and the number of infections in quarters on cows that did have a previous Staph. aureus infection. Furthermore, we calculated the number of infections that were cured at each sampling point.Estimation of Transmission Rates
Poisson regression is often used to estimate the transmission rates in studies of mastitis causing pathogens (e.g.,
where $\widehat{log\left({I}_{N}\right)}$ is the expected log number of new infections per sampling interval, β is the transmission rate, S_{int} is the number of susceptible quarter days at risk, I_{int} is the number of infectious quarter days, and N_{int} is the total number of lactating quarter days (see also
Zadoks et al., 2001a
; Leelahapongsathon et al., 2016
). However, 2 other methods were recently published and tested for precision against the Poisson regression (Kirkeby et al., 2017
). The 2 new methods proved better than Poisson regression when the transmission rate was high (above 0.025) and when the sampling intervals were large (about 2 wk). No regimens were found where the Poisson regression performed better than the 2 new methods. We used 3 methods for estimating the transmission rates for Staph. aureus to compare the estimated rates with those of previous studies and to use the 2 new methods that should perform better in some cases. The first method used was Poisson regression, which assumes that every newly infected individual (we regarded the quarters as individuals) is infected halfway between 2 sampling points. We calculated quarter days at risk between every sampling point. Deviating from the methods of Zadoks et al., 2001a
, we did not have farmercollected samples and clinical mastitis data available to adjust the quarter days at risk and infected quarter days: the number of susceptible quarters was multiplied by the length of the sampling interval, and the number of new infections multiplied by half of the length of the sampling interval was then subtracted. We included data on the dry off period and calving data for each cow to adjust the number of susceptible and infected quarters available, so that a cow would not be included in the analysis if it was not milking. Thus, we excluded all cows during the dry period and the first week postcalving. Likewise, we calculated the number of infected quarter days for each sampling period. We used the following equation for the Poisson regression:
$\widehat{log\left({I}_{N}\right)}=log\left(\beta \right)+log\left(\frac{{S}_{int}{I}_{int}}{{N}_{int}}\right),$
[1]
where $\widehat{log\left({I}_{N}\right)}$ is the expected log number of new infections per sampling interval, β is the transmission rate, S_{int} is the number of susceptible quarter days at risk, I_{int} is the number of infectious quarter days, and N_{int} is the total number of lactating quarter days (see also
Lam et al., 1996
). Confidence intervals were calculated as mean ±1.96 · SE.As mentioned above, we also used 2 recently described methods for estimating the transmission rate, named method 1 and method 2 for convenience (
where β is the transmission rate, IN is the number of new infections since the previous sampling, I is the number of infected quarters at each sampling point, T is the length of the sampling interval (days), S is the number of susceptible quarters at each sampling point, and N is the total number of animals at each sampling point. We therefore obtained an estimate of the transmission rate for each sampling interval.
Kirkeby et al., 2017
). These 2 methods do not make assumptions about the number of days the animals are present in the herd between the samplings. Furthermore, they only use information from the sampling points and are therefore more straightforward than the Poisson regression method. Therefore, it is not necessary to estimate the number of susceptible quarter days at risk or the number of infectious quarter days, and it is not necessary to use regression because a new estimate is calculated for each sampling interval. Because of these reasons, the new methods are simpler than the Poisson regression; however, it is still necessary to calculate the number of new infections for each sampling point. Practically, these methods are used to estimate the transmission rate for each sampling interval using equations [2] or [3], giving an estimate for each sampling interval. The overall estimate of the transmission rate for each of the 2 methods is then mean of these estimates. We first used method 1 to estimate the transmission rate for each sampling interval:
$\beta =\frac{log\left(1{I}_{N}/I\right)}{TS/N},$
[2]
where β is the transmission rate, IN is the number of new infections since the previous sampling, I is the number of infected quarters at each sampling point, T is the length of the sampling interval (days), S is the number of susceptible quarters at each sampling point, and N is the total number of animals at each sampling point. We therefore obtained an estimate of the transmission rate for each sampling interval.
Likewise, method 2 is given by
where the abbreviations are the same as in equation [2]. This method also yields an estimate of the transmission rate for each sampling interval. These 2 methods were derived to perform optimally under equilibrium conditions and do not assume that infections occur halfway between sampling points. Method 2 also allows for multiple infection and spontaneous cure events between sampling points. These 2 methods were previously evaluated on simulated IMI data and were found to perform as well as or better than the Poisson regression method (
$\beta =\frac{1}{T}log\left[1{I}_{N}\left(\frac{1}{I}+\frac{1}{S}\right)\right],$
[3]
where the abbreviations are the same as in equation [2]. This method also yields an estimate of the transmission rate for each sampling interval. These 2 methods were derived to perform optimally under equilibrium conditions and do not assume that infections occur halfway between sampling points. Method 2 also allows for multiple infection and spontaneous cure events between sampling points. These 2 methods were previously evaluated on simulated IMI data and were found to perform as well as or better than the Poisson regression method (
Kirkeby et al., 2017
). To derive confidence intervals for the transmission rate estimated for each sampling period using method 1 and method 2, we subsampled the quarter samples. We did this by sampling 75% of the quarters without replacement and calculating the transmission rate estimate for these quarters for each sampling point. We repeated this procedure 1,000 times to yield a proper estimate of the density distribution of the transmission rate. We then calculated the 95% confidence intervals for this distribution.In herd 1, the primiparous cows were kept separate from multiparous cows and milked separately, as described above. This presented the opportunity to subset the data and estimate the transmission rate in both subgroups of herd 1. We tested if the estimated distributions of transmission rates were different using a ztest.
We have included a practical example of the R code for estimating the transmission rates with the 3 different methods (Supplemental File; https://doi.org/10.3168/jds.201815106). We have also included the full code for the analyses in this study.
Estimation of the Duration of Infection
We investigated the duration of Staph. aureus infection at quarter level using the survfit function with default arguments in the survival package in R (
Therneau, 2015
). To estimate the duration of infection for subclinical cows, we calculated the duration of all new Staph. aureus quarter infections in the data. We used the register data with the dry period for all cows, as cows were not sampled during this period, to correct the data for the survival analysis. We assumed that quarters that were positive before and after the dry period were positive during the entire dry period. Quarters that were positive at dry off and negative after calving were considered to be cured at the sample after calving.To find the duration of infection, we conducted KaplanMeier survival analyses, following all new infections through the study period in both herds. We obtained the median duration of infection from the KaplanMeier analyses, taking into account that the data are right censored (e.g., when cows were culled or the study ended). Each infection was assumed to start halfway between 2 sampling points, and end halfway between 2 sampling points. After estimating the survival curves for Staph. aureus in each herd, we tested whether the curves were significantly different using a 2sample logrank MantelHaenszel test as per
Harrington and Fleming, 1982
.Basic Reproductive Ratio
We estimated the number of new Staph. aureus infections arising from one infectious individual (quarter) in each herd according to the procedure described by
where β is the transmission rate and τ is the duration of infection. For both herds, we extracted the mean and standard error from all 3 methods for estimating the transmission rate and used these to simulate 1,000 estimates of the transmission rate with the rnorm function in R. We then fitted an exponential function to the survival data using the lm function in R, and estimated the standard error around the mean from this function. We used the mean and standard error estimates to simulate 1,000 estimates of the duration of infection with the rnorm function in R. We then multiplied the 1,000 estimates of transmission rates with the 1,000 estimates of the duration of infection, creating a distribution of R_{0}. From this distribution, we extracted the mean and 95% confidence interval.
Lam et al., 1996
:
${R}_{0}=\beta \cdot \tau ,$
[4]
where β is the transmission rate and τ is the duration of infection. For both herds, we extracted the mean and standard error from all 3 methods for estimating the transmission rate and used these to simulate 1,000 estimates of the transmission rate with the rnorm function in R. We then fitted an exponential function to the survival data using the lm function in R, and estimated the standard error around the mean from this function. We used the mean and standard error estimates to simulate 1,000 estimates of the duration of infection with the rnorm function in R. We then multiplied the 1,000 estimates of transmission rates with the 1,000 estimates of the duration of infection, creating a distribution of R_{0}. From this distribution, we extracted the mean and 95% confidence interval.
RESULTS
In total, 7,466 milk samples were collected from herd 1 and 15,104 from herd 2 (Tables A1 to A4). In herd 1, a median of 217 quarters (160–252) were found to be infected with Staph. aureus at each sampling point (Table A1) and a median of 50 new quarter infections (9–73) were detected. This corresponds to a mean quarter prevalence of 34.0% (range = 25.6–40.9). In herd 1, only 1 sample on each of the dates 13.11.2017 and 11.12.2017 (date format: day, month, year) was found contaminated and discarded from the analysis. We observed 218 missing samples between 2 negative samples and 58 missing samples between a negative and a positive sample, which we corrected to be negative. The mean number of transient infections was 15.5 per sampling interval (mean = 7% of all infections at each sampling), and the mean number of cured infections was 30 per sampling interval (mean = 14% of all infections at each sampling). At cow level, a median of 110 cows (range = 88–122) were infected at each sampling, corresponding to a mean cowlevel prevalence of 69.3% (range = 56.8–84.0).
Table A1.Quarterlevel parameters used to estimate transmission rates of Staphylococcus aureus for herd 1
^{1}
Date format: day, month, year. Prev. = the quarterlevel prevalence; S = number of susceptible quarters; I = number of infected quarters; N = total number of quarters at risk (sampled); NI = new infections; NI.prev = number of new infections in quarters with previous Staph. aureus infection; NI.notprev = number of new infections in quarters without previous Staph. aureus infection; Corrected = number of negatives (assumed transiently infections) corrected to positive; Days = the number of days since the previous sampling; S.glm = number of susceptible quarter days at risk used for Poisson regression; I.glm = number of infected quarter days used for Poisson regression; N.glm = total number of quarter days used for Poisson regression; Method 1 and Method 2 indicate the estimated transmission rate per sampling interval; Transient = the number of transient infections; Cured = the number of cured infections.
Date  Prev.  S  I  N  NI  NI.prev  NI.notprev  Corrected  Days  S.glm  I.glm  N.glm  Method 1  Method 2  Transient  Cured 

16.01.2017  28.0  463  180  643  —  —  —  —  —  —  —  —  —  —  —  — 
13.02.2017  32.6  435  210  645  63  43  20  28  28  11,199  4,873  16,072  0.019  0.022  16  32 
14.03.2017  36.0  409  230  639  52  31  21  13  29  11,071  5,743  16,814  0.012  0.013  23  24 
10.04.2017  39.1  393  252  645  64  44  20  12  27  9,547  5,773  15,320  0.019  0.022  26  42 
08.05.2017  38.0  374  229  603  37  20  17  21  28  10,164  5,737  15,901  0.009  0.008  19  39 
12.06.2017  33.8  422  215  637  39  25  14  12  35  12,166  6,634.5  18,800.5  0.008  0.009  14  40 
10.07.2017  29.1  414  170  584  26  22  4  17  28  10,695  4,349  15,044  0.008  0.008  6  42 
14.08.2017  40.9  279  193  472  45  19  26  1  35  12,924  5,539  18,463.5  0.0124  0.014  15  9 
11.09.2017  25.6  465  160  625  9  7  2  27  28  11,007  4,206.5  15,213.5  0.003  0.003  1  28 
09.10.2017  34.0  424  218  642  73  42  31  9  28  11,041.5  4,821  15,862.5  0.019  0.021  20  8 
13.11.2017  35.9  427  239  666  56  33  23  23  35  12,637.5  6,899.5  19,537  0.013  0.015  15  28 
11.12.2017  34.9  433  232  665  50  34  16  —  28  10,088  5,540  15,628  0.015  0.017  —  35 
1 Date format: day, month, year. Prev. = the quarterlevel prevalence; S = number of susceptible quarters; I = number of infected quarters; N = total number of quarters at risk (sampled); NI = new infections; NI.prev = number of new infections in quarters with previous Staph. aureus infection; NI.notprev = number of new infections in quarters without previous Staph. aureus infection; Corrected = number of negatives (assumed transiently infections) corrected to positive; Days = the number of days since the previous sampling; S.glm = number of susceptible quarter days at risk used for Poisson regression; I.glm = number of infected quarter days used for Poisson regression; N.glm = total number of quarter days used for Poisson regression; Method 1 and Method 2 indicate the estimated transmission rate per sampling interval; Transient = the number of transient infections; Cured = the number of cured infections.
Table A4.Quarterlevel parameters used to estimate the transmission rates of Staphylococcus aureus in herd 2
^{1}
Date format: day, month, year. Prev. = the quarterlevel prevalence; S = number of susceptible quarters; I = number of infected quarters; N = total number of quarters at risk (sampled); NI = new infections; NI.prev = number of new infections in quarters with previous Staph. aureus infection; NI.notprev = number of new infections in quarters without previous Staph. aureus infection; Corrected = number of negatives (assumed transiently infections) corrected to positive; Days = the number of days since the previous sampling; S.glm = number of susceptible quarter days at risk used for Poisson regression; I.glm = number of infected quarter days used for Poisson regression; N.glm = total number of quarter days used for Poisson regression; Method 1 and Method 2 indicate the estimated transmission rate per sampling interval; Transient = the number of transient infections; Cured = the number of cured infections.
Date  Prev.  S  I  N  NI  NI.prev  NI.notprev  Corrected  Days  S.glm  I.glm  N.glm  Method 1  Method 2  Transient  Cured 

06.02.2017  3.1  1294  42  1336  —  —  —  —  —  —  —  —  —  —  —  — 
06.03.2017  3.0  1338  42  1380  10  3  7  6  28  34,323  1,008  35,331  0.010  0.010  4  6 
03.04.2017  3.1  1337  43  1380  10  5  5  1  28  36,110  1,012  37,122  0.010  0.0010  6  6 
01.05.2017  3.0  1346  41  1387  5  2  3  4  28  35,907.5  1,011  369,18.5  0.005  0.005  3  6 
06.06.2017  3.4  1273  45  1318  11  1  10  4  36  45,149  1,333.5  46,484.5  0.008  0.008  9  4 
03.07.2017  2.0  1256  26  1282  1  0  1  0  27  33,264.5  688.5  33,953  0.001  0.001  0  11 
07.08.2017  3.2  544  18  562  0  0  0  0  35  23,997  619  24,616  0  0  0  0 
04.09.2017  3.4  534  19  553  2  0  2  0  28  19,019  476  19,495  0.004  0.0041  1  1 
02.10.2017  1.0  1405  14  1419  0  0  0  1  28  21,551  353  21,904  0  0  0  6 
06.11.2017  1.0  1429  14  1443  3  0  3  1  35  47,167.5  367.5  47,535  0.007  0.007  3  3 
04.12.2017  1.8  1509  27  1536  9  0  9  1  28  37,492  454  37,946  0.015  0.0148  2  4 
08.01.2018  2.8  1469  43  1512  20  4  16  —  35  48,059.5  845  48,904.5  0.018  0.019  —  13 
1 Date format: day, month, year. Prev. = the quarterlevel prevalence; S = number of susceptible quarters; I = number of infected quarters; N = total number of quarters at risk (sampled); NI = new infections; NI.prev = number of new infections in quarters with previous Staph. aureus infection; NI.notprev = number of new infections in quarters without previous Staph. aureus infection; Corrected = number of negatives (assumed transiently infections) corrected to positive; Days = the number of days since the previous sampling; S.glm = number of susceptible quarter days at risk used for Poisson regression; I.glm = number of infected quarter days used for Poisson regression; N.glm = total number of quarter days used for Poisson regression; Method 1 and Method 2 indicate the estimated transmission rate per sampling interval; Transient = the number of transient infections; Cured = the number of cured infections.
In herd 2, a median of 34 (14–45) quarters were found to be infected with Staph. aureus at each sampling point and a median of 5 new quarter infections (0–20) were detected (Table A4). This corresponds to a mean quarter prevalence of 2.57% (range = 1–3.4). In herd 2, only 1 sample on each of the dates 06.03.2017, 07.08.2017, and 04.09.2017 was found contaminated and discarded from the analysis. We noted 573 missing samples between 2 negative samples and 12 missing samples between a negative and a positive sample, which we assumed to be negative. The mean number of transient infections was 2.8 per sampling interval (mean = 8% of all infections at each sampling), and the mean number of cured infections was 5.5 per sampling interval (mean = 18% of all infections at each sampling). At cow level, a median of 25.4 cows (range = 12–39) were infected at each sampling, corresponding to a mean cowlevel prevalence of 11.4% (range = 3.3–30.6).
In Figure 1, we show the DIM where new infections occur. In herd 1, a peak of new infections occurred between 50 and 150 DIM and then declined. In herd 2, a peak in new infections occurred around 50 to 100 DIM and another peak occurred between 200 and 350 DIM.
Transmission Rates
The estimated transmission rates are shown in Table 3. In herd 1, the transmission rate was estimated to be 0.0128 cases/quarter day for all cows, with 95% confidence interval of 0.01019 and 0.0162 cases/quarter day using Poisson regression. All 3 methods yielded similar estimates.
Table 3Estimated transmission rates (95% CI) for Staphylococcus aureus from herds 1 and 2 and the subpopulations in herd 1 (herd 2 was not divided into subpopulations)
Herd  Population  Poisson regression  Method 1  Method 2  Mean  

1  All cows  0.0128 (0.01019–0.0162)  0.0128 (0.0042–0.0213)  0.0140 (0.0043–0.0242)  0.0132  
Primiparous  0.0129 (0.0102–0.0164)  0.0123 (0.0027–0.0204)  0.0133 (0.0028–0.0230)  0.0128  
Multiparous  0.0130 (0.0108–0.0168)  0.0133 (0.0046–0.0247)  0.0149 (0.0048–0.0300)  0.0137  
2  All cows  0.0089 (0.0055–0.0145)  0.0071 (0–0.0175)  0.0072 (0–0.0176)  0.0077 
Using all 3 methods, the transmission rates for primiparous cows in herd 1 were found to be similar to those for multiparous cows, indicating a similar infection pressure for both groups. This was supported by a ztest performed for each of the 3 estimation methods. All 3 tests showed no significant difference (data not shown).
The mean transmission rate for herd 2 was estimated to be on average 0.0077 cases/quarter day, almost half that of herd 1 (Table 3). All 3 methods yielded similar results: the Poisson regression estimated the rate at 0.0089 cases/quarter day, whereas method 1 and method 2 estimated 0.0071 and 0.0072 cases/quarter day, respectively. The confidence limits for the Poisson regression estimate were narrower than those for the 2 other methods (Table 3).
Using methods 1 and 2, we obtained an estimate of the transmission rate for each sampling interval (Tables A1, A2, Table A3., Table A4.) and can therefore explore the variation in the transmission rate over the study period (Figure 2). In herd 1, the estimated transmission rate varied, but decreased and then plateaued from May onwards. This plateau more or less continued until September, when we observed a large decrease. A high peak followed in October, and the rate seemed to increase slightly from the low plateau. This pattern was found for both the primiparous and the multiparous cows in herd 1. We noted a similar pattern in herd 2, with a lower transmission rate between May and October but with variation and minor peaks. From October, the transmission rate seemed to increase and surpass the level at the beginning of the study.
Table A2.Quarterlevel parameters used to estimate the transmission rates of Staphylococcus aureus for primiparous cows in herd 1
^{1}
Date format: day, month, year. Prev. = the quarterlevel prevalence; S = number of susceptible quarters; I = number of infected quarters; N = total number of quarters at risk (sampled); NI = new infections; Days = the number of days since the previous sampling; S.glm = number of susceptible quarter days at risk used for Poisson regression; I.glm = number of infected quarter days used for Poisson regression; N.glm = total number of quarter days used for Poisson regression; Method 1 and Method 2 indicate the estimated transmission rate per sampling interval.
Date  Prev.  S  I  N  NI  Days  S.glm  I.glm  N.glm  Method 1  Method 2 

16.01.2017  23.4  164  50  214  —  —  —  —  —  —  — 
13.02.2017  30.5  146  64  210  22  28  3962  1,484  5,546  0.022  0.024 
14.03.2017  31.2  141  64  205  13  29  3852.5  1,632.5  5,485  0.011  0.012 
10.04.2017  31.2  148  67  215  15  27  3516  1,498.5  5,014.5  0.014  0.015 
08.05.2017  32.8  127  62  189  13  28  3503  1,526  5,029  0.013  0.013 
12.06.2017  23.3  178  54  232  9  35  4054.5  1,487.5  5,542  0.007  0.007 
10.07.2017  20.3  153  39  192  4  28  4126  1,036  5,162  0.005  0.005 
14.08.2017  31.9  113  53  166  17  35  4568  1,487.5  6,055.5  0.016  0.018 
11.09.2017  20.5  174  45  219  2  28  3529  1,134  4,663  0.002  0.002 
09.10.2017  23.3  174  53  227  14  28  4046  1,232  5,278  0.014  0.015 
13.11.2017  27.7  172  66  238  23  35  4970  1,750  6,720  0.017  0.019 
11.12.2017  26.3  182  65  247  17  28  3976  1,470  5,446  0.015  0.016 
1 Date format: day, month, year. Prev. = the quarterlevel prevalence; S = number of susceptible quarters; I = number of infected quarters; N = total number of quarters at risk (sampled); NI = new infections; Days = the number of days since the previous sampling; S.glm = number of susceptible quarter days at risk used for Poisson regression; I.glm = number of infected quarter days used for Poisson regression; N.glm = total number of quarter days used for Poisson regression; Method 1 and Method 2 indicate the estimated transmission rate per sampling interval.
Table A3.Quarterlevel parameters used to estimate the transmission rates of Staphylococcus aureus for multiparous cows in herd 1
^{1}
Date format: day, month, year. Prev. = the quarterlevel prevalence; S = number of susceptible quarters; I = number of infected quarters; N = total number of quarters at risk (sampled); NI = new infections; Days = the number of days since the previous sampling; S.glm = number of susceptible quarter days at risk used for Poisson regression; I.glm = number of infected quarter days used for Poisson regression; N.glm = total number of quarter days used for Poisson regression; Method 1 and Method 2 indicate the estimated transmission rate per sampling interval.
Date  Prev.  S  I  N  NI  Days  S.glm  I.glm  N.glm  Method 1  Method 2 

16.01.2017  30.3  299  130  429  —  —  —  —  —  —  — 
13.02.2017  33.6  289  146  435  41  28  7,333  3,389  10,722  0.018  0.020 
14.03.2017  38.2  268  166  434  39  29  7,376  4,101.5  11,477.5  0.015  0.017 
10.04.2017  43.0  245  185  430  49  27  6,091  4,274.5  10,365.5  0.020  0.023 
08.05.2017  40.3  247  167  414  24  28  6,606.5  4,211  10,817.5  0.009  0.010 
12.06.2017  39.8  244  161  405  30  35  8,252.5  5,135  13,387.5  0.010  0.011 
10.07.2017  33.4  261  131  392  22  28  6,571  3,266  9,837  0.010  0.010 
14.08.2017  45.8  166  140  306  28  35  8,349.5  4,106  12,455.5  0.012  0.013 
11.09.2017  28.3  291  115  406  7  28  7,280  3,072.5  10,352.5  0.003  0.003 
09.10.2017  39.8  250  165  415  59  28  6,795.5  3,609  10,404.5  0.026  0.032 
13.11.2017  40.0  259  173  432  33  35  7,667.5  5,149.5  12,817  0.010  0.011 
11.12.2017  40.0  251  167  418  33  28  6,112  4,070  10,182  0.013  0.014 
1 Date format: day, month, year. Prev. = the quarterlevel prevalence; S = number of susceptible quarters; I = number of infected quarters; N = total number of quarters at risk (sampled); NI = new infections; Days = the number of days since the previous sampling; S.glm = number of susceptible quarter days at risk used for Poisson regression; I.glm = number of infected quarter days used for Poisson regression; N.glm = total number of quarter days used for Poisson regression; Method 1 and Method 2 indicate the estimated transmission rate per sampling interval.
Survival Analysis
KaplanMeier analyses showed that the median duration of infection in herd 1 was 91 d (95% CI = 90–119; Figure 3A). The mean duration of infection was 161.5 with a standard error of 6.9. In herd 2, the median duration of infection was 64 d (95% CI = 36 to not applicable; Figure 3B) and the mean estimate was 112.1 with a standard error of 16.1. We found that the survival curves did not differ significantly using a logrank test (P = 0.1).
R_{0}
Table 4 shows the estimated R_{0} for herd 1 and herd 2 using the different estimation methods. Using the Poisson method, R_{0} was estimated at 1.16 (95% CI = 0.93–1.45) in herd 1. This indicates that, on average, an infected quarter would infect 1.16 other quarters during its entire infectious period within an entirely susceptible population. Similar estimates were observed using the 2 other estimation methods, and the mean of the 3 methods was 1.21 (Table 4). The confidence intervals of the estimates from the 3 methods overlap. In herd 2, the mean R_{0} was found to be 0.52 (Table 4).
Table 4The estimated reproductive ratio (R_{0}) for each herd in the study; mean values with 95% CI are shown in parentheses
Herd  Poisson regression  Method 1  Method 2  Mean 

1  1.16 (0.93–1.45)  1.16 (0.20–2.13)  1.30 (0.18–2.42)  1.21 
2  0.59 (0.35–0.94)  0.48 (0–1.24)  0.48 (0–1.23)  0.52 
DISCUSSION
The transmission rate of IMIcausing pathogens is an important parameter when using simulation models to predict the costeffectiveness of strategies to prevent and control these pathogens within dairy cattle herds. However, transmission dynamics are rarely studied in the field, because such studies are timeconsuming and costly. Consequently, few studies have analyzed the transmission dynamics in dairy cattle herds. Therefore, our aim was to investigate these dynamics in 2 fairly large Danish dairy herds with low and high IMI prevalence (
Roberson et al., 1994
, Graber et al., 2009
).The quarterlevel prevalence in our study was 34 and 2.57% for herds 1 and 2, respectively (Table A1., Table A4.). In previous studies of dairy herds, the quarterlevel prevalence of Staph. aureus was shown to differ among herds.
Sommerhäuser et al., 2003
found a prevalence of 4.2 to 11.9% in herds with moderate or high Staph. aureus problems and 24.2 to 27.1% in herds with high levels of Staph. aureus IMI. Schwarz et al., 2010
described a prevalence of 5.01% across herds in one German federal state. From these results, herd 1 in our study reflects a herd with a high prevalence of Staph. aureus and herd 2 reflects a herd with a low prevalence of Staph. aureus.The estimated transmission rates indicate that herd 1 had a considerably higher transmission rate than herd 2; the median number of new infections per sampling round was 50 for herd 1 (Table A1) and 5 for herd 2 (Table A4). If we consider the estimate using Poisson regression, as in previous studies, the estimated transmission rates were 0.0128 and 0.0089 cases per quarter day for herds 1 and 2, respectively. Using Poisson regression,
Lam et al., 1996
estimated the transmission rate in a herd to be 0.046 cases/quarter day during an outbreak and 0.0063 cases/quarter day outside the outbreak period. The estimated transmission rates in our study are therefore lower than those found by Lam et al., 1996
during an outbreak. Zadoks et al., 2002
estimated the transmission rate to be 0.007 cases/quarter day and 0.014 cases/quarter day in different herds with a Staph. aureus problem, giving similar results to those presented here, although the herds studied in Zadoks et al., 2002
were considerably smaller (67, 95, and 41 cows) than in our study. This indicates that Staph. aureus can express similar behavior in dairy herds from different countries or regions, even though certain management practices may be different, as blanket dry cow therapy was used in the Netherlands at that time (Zadoks et al., 2002
) whereas selective dry cow therapy is used in Denmark.Barlow et al., 2013
estimated the transmission rate for Staph. aureus at 0.00804 cases/quarter day and 0.00448 cases/quarter day for 2 different herds. Schukken et al., 2014
estimated a monthly quarterlevel transmission rate at 0.295, corresponding to 0.009 per quarter day. van den Borne et al., 2017
estimated a cowlevel transmission rate at 0.0232. The estimated rates in our study are therefore similar to some of the previous findings. The herds in the studies by Lam et al., 1996
and Barlow et al., 2013
used both blanket dry cow therapy and premilking teat dipping, whereas the herds in this study used selective dry cow therapy and postdipping was used in herd 1. The environmental and milking hygiene level in herd 1 were quite poor and did not change throughout the study period, which was reflected by the high transmission rate within this herd. This information is useful when studying the economic consequences of control actions under different endemic levels of IMI. Nevertheless, herd 1 in our study should start by improving general hygiene, especially at milking, to reduce the infection pressure, before implementing actions such as treatment during lactation and culling, as suggested by Barlow et al., 2009
and by van den Borne et al., 2010
.In herd 1, we estimated the transmission rate for both primiparous and multiparous cows and found no significant difference between the 2 subpopulations. It has previously been indicated that parity is a risk factor for IMI and clinical IMI, and that multiparous cows have higher risk of infection than primiparous cows (
Steeneveld et al., 2008
; Breen et al., 2009
). However, this could also be an effect of older cows simply being exposed for longer time or having a lower probability of cure and therefore being infected more often. The estimated transmission rate is affected by the mastitis management of the herd, susceptibility of animals, pathogen strain type (which was not included in the present study), and the contact rate between animals, which might differ between farms but should be fairly consistent within each farm (McCallum et al., 2001
). Zadoks et al., 2001b
actually found that, at quarter level, the difference in risk of infection with Staph. aureus between primiparous cows and multiparous cows (here cows with parity >2) was herdspecific. The risk was statistically significant in 1 of the 3 studied herds, which could be a result of the management practices of the herd. This clearly indicates that modeling the spread of Staph. aureus as well as its control and prevention should be herdspecific, as differences in management between herds could affect the transmission dynamics and possibly the costeffectiveness of the control strategies.The estimated transmission rate showed peaks in the spring and autumn (Figure 2) in both herds included in our study. Transmission therefore seems to be lower during the summer, indicating seasonality in the spread of Staph. aureus (Table A1., Table A4.). Earlier surveys are consistent with our findings, and Staph. aureus was not found to be an IMI problem in summer, when Corynebacterium pyogenes or Escherichia coli were more often reported (
Hillerton, 1987
; Waage et al., 1999
). Farmers could use this information to focus intervention strategies during the winter to reduce the spread of Staph. aureus among animals. Cases of Staph. aureus clinical IMI have been shown to be the most expensive clinical cases due to high milk loss (Cha et al., 2014
).We estimated the median duration of subclinical Staph. aureus infections to be 91 and 64 d in herds 1 and 2, respectively. In the logrank test, the curve for the duration of infection was not found to differ significantly (P > 0.05) between the 2 herds. The duration of infection is affected by the strain type of the bacteria (
Haveri et al., 2005
) and by the ability of the farmer to detect and treat or cull infected animals. Methods for detecting subclinically infected cows include evaluating the milk production and the SCC followed by diagnostic testing. The farmer should ideally then follow up on individual cows with high SCC. In both herds, most of the infections lasted between 1 and 2 mo (Figure 4), showing that the cows are continuously infected in short periods. In herd 1, the proportion of longerlasting infections was higher, which is reflected in the estimated duration of infection. Lam et al., 1996
estimated the mean duration of infection to be 136 d. Zadoks et al., 2002
estimated the daily cure rate to be 0.0052, 0.0157, and 0.0119 for each quarter; converting these to duration of infection (1/cure rate) gives 192, 64, and 84 d, respectively. Our findings of duration of infection are clearly consistent with the findings of Lam et al., 1996
and Zadoks et al., 2002
.In Figure 1, the DIM where new infections occur is shown. In both herds, we noted a peak of new infections just after 50 DIM, but in herd 2 we also found a peak in infections between 200 and 350 DIM. This could indicate a difference in transmission dynamics between the 2 herds. Effectively, a larger proportion of the infections in herd 2 appears later in the lactation, and therefore they are more likely to be cured earlier, at dry off, following dry off treatment. This results in a lower probability of transmission between animals in the herd, reducing the prevalence. Moreover, this is also reflected in the estimated duration of infection, which was lower in herd 2 compared with herd 1.
The duration of infection found in this and other studies showed that the sampling interval used in the present study was appropriate. The sampling interval should not exceed the duration of infection because this could allow for infection and recovery between samplings (
Kirkeby et al., 2017
). However, it is still possible that some infections remain undiscovered because the duration of infection is a distribution and, hence, some infections will be shorter than the average and the sampling interval.We corrected missing samples between a positive and a negative sample to negative; this will underestimate the duration of infection if the missing sample was positive. However, we chose this procedure in order not to inflate the duration of infection. Furthermore, given the limited number of missing values compared with the total number of samples, this was not expected to affect the estimated parameters significantly.
Missing data on the treatment of clinical animals is also a limitation of our study. A complete record of the treatment data would enable the estimation of the spontaneous cure rate, the treatment cure rate, and the flareup rate from subclinically to clinically infected cases. These parameters are also important in bioeconomic models of IMI. Although the farmers were asked repeatedly to register and sample clinical cases and register treatments, this was done only occasionally, impeding the chance to estimate these parameters.
As mentioned by
Leelahapongsathon et al., 2016
, the precision of the results may be improved by examining large herds. The noise of stochastic infection events is lower in large herds, because in the models used to estimate parameters we assume that the infection status is basically a binomial process based on underlying probabilities (Kirkeby et al., 2017
). The estimated transmission rates and duration of infection presented in our study are valuable for investigating costeffective measures against IMI caused by Staph. aureus in dairy cattle herds.CONCLUSIONS
We investigated the transmission dynamics of Staph. aureus IMI at quarter level in 2 Danish dairy herds. We found a quarterlevel prevalence of 34 and 2.57% for herd 1 and 2, respectively. Furthermore, we estimated the daily quarterlevel transmission rate to be 0.0132 and 0.0077 cases/quarterday for herd 1 and 2, respectively. The duration of infection was estimated to be 91 and 64 d, and we calculated the R_{0} to be 1.21 and 0.52 for the 2 herds for herd 1 and 2, respectively. These estimates can be used to parameterize models simulating the spread of Staph. aureus, to assess the costeffectiveness of strategies to prevent and control IMI caused by Staph. aureus within dairy cattle herds.
ACKNOWLEDGMENTS
We thank the participating farmers and the teams from SEGES, Registrerings og Ydelseskontrol (RYK), Skejby, Denmark, and FOSS for helping with data acquisition, Kaare Græsbøll (DTU Compute, Denmark) and Matt Denwood (Department of Veterinary and Animal Sciences, University of Copenhagen, Denmark) for discussion on the analyses, and Karen Schlez and Tobias Eisenberg at LHL laboratories for bacterial culture and identification of pathogens (LHL, Gießen, Germany). This project was funded by the Green Development and Demonstration Program (GUDP) under the Danish Directorate for Food, Fisheries and Agriculture (Copenhagen, Denmark), grant no. 34009150918 (EMCoMAST project).
APPENDIX

Supplementary Material
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Article info
Publication history
Published online: December 26, 2018
Accepted:
October 19,
2018
Received:
May 23,
2018
Identification
Copyright
© 2018 American Dairy Science Association®.