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1.
A total of 796 sows and gilts from 30 Danish sow herds were examined three times at intervals of 6 weeks for serum antibodies to Leptospira bratislava by the microscopic agglutination technique (MAT) test. The prevalence of seroreactors with positive titer values, 1:100, at the three successive tests were 2.7%, 2.5% and 2.9%; 4.5% of the animals were positive in at least one of the three tests, and 2.2% showed a greater than two-fold rise in titer between two consecutive samplings. Of the 30 herds, 21 (70%) had ever-positive within-herd prevalences in sows and gilts of 4–13%. The risk of a herd having one or more positive sow was positively associated with a herd size of > 141 sows, and distinct regional differences in the prevalence of positive herds were observed. The reproductive performance of the 21 herds with seroreactions was poorer than the performance of the nine herds without positive reactions concerning the variables: ‘days from weaning to last service’ (2.7 days more, P = 0.07), ‘percentage of sows returning to heat’ (4.0 percentage units more, P = 0.03), ‘services per farrowing’ (0.04 more, P = 0.04), ‘farrowing percentage’ (4.3 percentage units lower, P = 0.06), and ‘stillborn pigs per farrowing’ (0.16 more, P = 0.02). No association between the MAT serological status of the herd and the incidence of medical treatments of sows and gilts could be found. A high prevalence and low cumulative incidence of seroreactors was demonstrated in first-parity gilts, followed by a low prevalence and cumulative incidence from parity 2 to 3, and a high prevalence and cumulative incidence at the fifth parity.  相似文献   

2.
A retrospective cohort study of Irish cattle herds investigated whether the severity of a herd’s bovine tuberculosis (BTB) breakdown was a predictor of the hazard of a future BTB breakdown in that herd. Data on 10,926 herds not having had BTB in 1995 (the “non-exposed” group) were obtained using a 10% random sample from all herds without BTB in 1995. Data on 6757 herds that had a new BTB breakdown in 1995 (the “exposed” group) were obtained and categorized into five increasing exposure-severity classes based on the total number of standard reactors (to the single intra-dermal comparative cervical tuberculin test) detected during the breakdown. Exposed herds were deemed to be free of BTB after they passed a 6-month check test; non-exposed herds were deemed free as of the date of the first negative herd-test in 1995.

In the 5 years after 1995, 18% of the non-exposed herds had a BTB breakdown, whereas 31% of the exposed herds had a subsequent breakdown. Relative to the hazard for non-exposed herds, the hazard for the first future singleton standard reactor breakdown, was 1.6-times higher for exposed herds with only 1 standard reactor in 1995, and 1.8-times higher for those exposed herds with 4–8 standard reactors during the 1995 episode. When the outcome for future breakdowns was 2 or more standard reactors, the hazard ratios ranged from 1.6 for exposed herds with only 1 standard reactor in 1995 up to 2.9 in exposed herds with 8 or more standard reactors during the 1995 episode. The latter hazard ratio varied over time, decreasing to 1.7 after 3 years of risk. The hazard of a future BTB breakdown increased directly with number of cattle in the herd, a positive history of previous BTB in the herd, and the local herd prevalence of BTB. The presence of confirmed BTB lesions in reactor cattle was not predictive of the future breakdown hazard when the effects of other factors were controlled.  相似文献   


3.
In Ireland, the herd prevalence of bovine tuberculosis has remained stable for several decades, and in common with several other countries, progress towards eradication has stalled. There is evidence in support of the potential role of infected badgers (Meles meles, a protected species) in bovine tuberculosis in Ireland and Britain. However, this evidence on its own has not been sufficient to prove disease causation. Field trials are likely to offer the best opportunity to define this role. Building on the earlier East Offaly project, our objectives were to assess the impact of badger removal on the control of tuberculosis in cattle herds in Ireland.

The study was conducted from September 1997 to August 2002 in matched removal and reference areas (average area of 245.1 km2) in four counties: Cork, Donegal, Kilkenny and Monaghan. Badger removal was intensive and proactive throughout the study period in the removal areas, but reactive (in response to severe tuberculosis outbreaks in cattle) in the reference areas. Removal intensity in the removal and reference areas during the first 2 years of the study averaged 0.57 and 0.07 badgers/km2/year, respectively.

The outcome of interest was restriction of cattle herds due to confirmed tuberculosis, where tuberculous lesions were detected in one or more animals. Data were analysed using logistic regression (modelling the probability of a confirmed herd restriction) and survival analysis (modelling time to a confirmed herd restriction).

During the study period, there was a significant difference between the removal and reference areas in all four counties in both the probability of and the time to a confirmed herd restriction due to tuberculosis. In the final year of the study, the odds of a confirmed herd restriction in the removal (as compared to the reference areas) were 0.25 in Cork, 0.04 in Donegal, 0.26 in Kilkenny and 0.43 in Monaghan. Further, the hazard ratios (removal over reference) ranged from 0.4 to 0.04 (a 60–96% decrease in the rate at which herds were becoming the subject of a confirmed restriction).  相似文献   


4.
The objective of the study was to estimate the range of influence between cattle herds with positive Salmonella Dublin herd status. Herd status was a binary outcome of high/low antibody levels to Salmonella Dublin in bulk-tank milk and blood samples collected from all cattle herds in Denmark for surveillance purposes. Two methods were used. Initially, a spatial generalised linear mixed model was developed with an exponential correlation function to estimate the range of influence simultaneously with the effect of potential risk factors. An iteratively reweighted generalised least squares procedure was used as a second method for verifying the range of influence estimates. With this iterative procedure, deviance residuals were calculated based on a generalised linear model and the range of influence was estimated based on the residuals using an exponential semivariogram. The range of influence was estimated for six different regions in Denmark using both methods. The analyses were performed on data collected during 1 year after initiation of the Salmonella Dublin surveillance program providing herd classifications for the 4th year-quarter of 2003 and 2 years later for the 4th year-quarter of 2005. The prevalence of dairy herds with a positive Salmonella Dublin herd classification status in this period had decreased from 22.1 to 17.0%. In non-dairy herds, the prevalence was nearly unchanged during the same period (3.4 and 3.7% in 4th quarter of 2003 and 2005, respectively). For all cattle herds, the range of influence was 2.3–6.4 km in 2003 and 1.5–8.3 km in 2005. There seemed to be no association between the range of influence and the density of herds in the different regions.  相似文献   

5.
In each of 42 Danish dairy herds, ten young stock aged 8–18 months were tested for antibodies against bovine virus diarrhoea virus (BVDV). At the same time a bulk milk sample from each herd was examined for antibodies against BVDV.

The herds could be divided into two distinct groups: (1) Group A (24 herds) had three or less antibody carriers among the ten young stock sampled from each herd and were considered ‘slightly infected’; (2) Group B (18 herds) had eight or more antibody carriers in the ‘spot’ sample and were therefore considered ‘heavily infected’. Persistently infected animals were not found in two Group A herds studied by a subsequent total herd blood test but were detected in five Group B herds in which all animals in the herds were subsequently tested.

Bulk milk titers were generally higher in Group B than in Group A herds. However, there was considerable variation, and in most cases it was not possible to distinguish the two herd categories from one another by means of bulk milk titers.  相似文献   


6.
Prior to establishing a control and prevention program for Johne's disease in cattle in Galicia (northwest Spain), a survey was conducted to estimate the prevalence of the disease. For this survey, 61,069 animals of at least 1-year of age from 2735 randomly selected herds were bled and samples analyzed with a commercial ELISA. The estimated true individual-level prevalences – assuming the manufacturer's reported test sensitivity of 48.5% and specificity of 98.9% – were 3.02% in dairy cattle, 1.03% in beef cattle and 2.83% in animals from farms with both dairy and beef cattle. True herd prevalences (with herds declared positive if one or more animals tested positive) were 10.69% for dairy herds, 0% for beef herds and 2.71% for mixed herds. When herds were declared positive if at least two animals tested positive, true herd prevalences were 14.75% for dairy herds, 1.47% for beef herds and 12.01% for mixed herds. Assuming a higher specificity of 99.4%, true individual-level prevalences increased to 4.03% in dairy herds, 2.07% in beef herds and 3.84% in mixed herds. Herd prevalences were 27.77%/18.79%, 2.78%/2.40% and 5.70%/12.24% (using the one/two-animal cut-offs) in dairy, beef and mixed herds, respectively. In conclusion, these results seem to indicate that a small percentage of cows and a rather high percentage of dairy herds in this region are MAP-seropositive.  相似文献   

7.
8.
A cross-sectional study was conducted from June through December 1996 to identify management-related risk factors for herd-level M. paratuberculosis infection. Data were collected from 121 participating herds. A two-part questionnaire was administered to gather data on current and previous management practices and herd productivity. A random sample of cows aged ≥24 months was selected from each herd and tested for antibodies to M. paratuberculosis using the IDEXX Antibody ELISA (sensitivity 64%, specificity 96%). A positive herd was one in which ≥2 animals tested positive for antibodies to M. paratuberculosis. A negative herd was one in which no animal tested positive. Herds in which only one animal tested positive were dropped from statistical analysis to reduce the risk of including false-positive herds in the statistical analyses.

There were 80 herds with one or more positive animals and 41 herds with no positive animals in the sample (66% herd-level prevalence). Twenty-six herds (21%) were dropped from further analyses because they had only one positive cow. Twelve herds (10%) were dropped from analysis because of missing data. The resulting sample used for statistical modeling included 46 positive herds and 37 negative herds (55% herd-level prevalence). A multi-variable logistic-regression model was used to evaluate the results. The variable ‘use of an exercise lot for lactating cows' was associated with a three-fold increase in odds of a herd being positive for M. paratuberculosis infection (O.R.=3.01, C.I.=1.03–8.80); ‘cleaning of maternity pens after each use' was associated with a three-fold reduction in odds of a herd being positive for M. paratuberculosis infection (O.R.=0.28, C.I.=0.08–0.89); ‘application of lime to pasture areas in 1993' resulted in a ten-fold decrease in odds of a herd being positive for M. paratuberculosis infection (O.R.=0.10, C.I.=0.02–0.56).  相似文献   


9.
Associations of the occurrence of Ascaris suum and Oesophagostomum spp. in sows with herd management factors were examined using logistic-binomial regression. The information used was from 11 to 78 sows sampled from each of 83 breeding herds (2961 sows in total) and examined for eggs per gram of faeces (EPG). A sow excreting at least 20 EPG was defined as ‘infected’. Management factors of the study herds were recorded using a questionnaire. A total of 263 sows from 50 herds (8.9% of sows) and 375 sows from 20 herds (12.7% of sows) were infected with A. suum and Oesophagostomum spp., respectively. For A. suum, sows from herds with more than 85 sows had significantly higher odds of being infected compared with those from 30 to 85 sows (P < 0.05). When bedding was provided for sows, the odds of A. suum infection was 5.4 compared with sows from herds in which bedding was not provided (P < 0.05). For Oesophagostomum spp., sows from herds with different specific pathogen free status had about one tenth the odds of being infected compared with those from conventional herds (P < 0.05). Sows that had been treated with anthelmintics had very low odds of being infected with Oesophagostomum spp. compared with those that were not treated (P < 0.05). The effects of these management factors in both final models did not differ when the definition of an ‘infected’ sow was changed. The present results suggest the importance of disposal of bedding material from pens in reducing the prevalence of A. suum in larger sow herds. Anthelmintic treatment is important in reducing the prevalence of Oesophagostomum spp. infection of sows.  相似文献   

10.
Sixty-one Mycobacterium avium subsp. paratuberculosis isolates from cattle and deer from the Buenos Aires province, an important livestock region in Argentina, were typed by restriction fragment length polymorphisms (RFLP) analysis based on IS900. Four different RFLP patterns (designated ‘A’, ‘B’, ‘C’ and ‘E’) were identified in BstEII digests of genomic DNA. The most frequently observed type, pattern ‘A’, was found in 46 isolates (75%). The second, pattern ‘E’, included 8 isolates (13%), while the third, pattern ‘B’, included 6 isolates (10%). Pattern ‘C’ was found for only one isolate. All of the deer isolates were classified as pattern ‘A’, while cattle isolates represented all four RFLP patterns. Twenty-one isolates representing the four different BstEII-RFLP patterns were digested with PstI. Twenty isolates showed identical PstI-RFLP pattern. BstEII-RFLP patterns from Argentine cattle and deer were compared with patterns found in cattle, goat, deer, rabbit, and human isolates from Europe. The most common pattern in Argentina, pattern ‘A’, was identical to a less frequently occurring pattern R9 (C17) from Europe. The other Argentine patterns ‘B’, ‘C’ and ‘E’, were not found in the Europe. These results indicate that the distribution of M. avium subsp. paratuberculosis genotypes in the Buenos Aires province of Argentina is different from that found in Europe.  相似文献   

11.
12.
We analysed the individual-animal data from six of the nine outbreaks of tuberculosis in Canadian cattle and cervids from 1985 to 1994. A “positive/reactor” animal was one which had either a positive culture or a positive or suspicious reaction on a mid-cervical, comparative cervical, or gross or histopathological test for tuberculosis. Individual-animal data were collected only for herds which had one or more positive/reactor animals. Data were collected from the outbreak records in the Regional or District offices of Agriculture and Agri-food Canada’s Animal and Plant Health Directorate. The within-herd spread of Mycobacterium bovis was studied by determining the most-likely date at which the herd was first exposed to M. bovis and the number of reactions which had developed by the time the herd was investigated. The animal-time units at risk in the herd were probably overestimated, resulting in conservative estimates of the within-herd incidence rates. Negative-binomial regression was used to investigate factors which might have influenced the within-herd spread of tuberculosis. Increasing age appeared to be a risk factor for being a positive/reactor animal. When compared to animals 0–12 months old, animals 13–24 months old had an incidence rate ratio (IRR) of 7.6, while animals >24 months old had an IRR of 10.4 (p=0.009). Actual and predicted incidence rates for tuberculosis in mature (>24 months old) animals were calculated. Actual and predicted incidence rates were similar for cervids, within an outbreak. There was more variability between actual and predicted rates in the dairy and beef animals. In the one outbreak (Ontario) where there were positive/reactor cervid, dairy and beef herds, the actual incidence rate for cervids (IR=9.3 cases per 100 animal-years) was almost twice that of dairy cattle (IR=5.0) and three times that of beef cattle (IR=3.1).  相似文献   

13.
In Denmark, the detection of multi-resistant Salmonella Typhimurium DT104 (MRDT104)-infected pig herds relies on the national Salmonella surveillance programme at the farm and slaughterhouse levels of production. With the surveillance sampling protocol and the diagnostic methods currently used, some herds might remain undetected. The number of undetected Danish pig herds infected with MRDT104 in the period 1 August 2001–31 July 2002 was estimated and compared with the number of culture-confirmed detected herds. A flow chart was constructed to illustrate where infected herds will go undetected in the surveillance system and Monte Carlo simulation was used to model the actual number of pig herds infected with MRDT1104. We estimated that 52 (90% CI [28, 178]) finisher herds were infected with MRDT104 compared to 23 (44%) detected. Among sow herds with production of weaners or growers, we estimated that 38 (90% CI [23, 74]) were infected with MRDT104 compared to 7 (18%) actually detected. Among breeder and multiplier herds, we estimated that five (90% CI [3, 8]) herds were infected with MRDT104 compared to three (60%) detected. In total, we estimated that 102 pig herds were infected with MRDT104 from 1 August 2001 till 31 July 2002 (90% CI [63, 228]). In comparison, 33 (32%) infected herds were detected in this period. The predicted proportion of undetected herds varied considerably with herd type. We infer that the proportion of detected MRDT104 infected herds depended on the intensity of the combined serological and bacteriological testing.  相似文献   

14.
In this study, we describe a method to quantify the transmission of Classical Swine Fever Virus (CSFV) between herds from data collected during the 1997–1998 epidemic in the Netherlands. From the contacts between infected herds and the serological findings shortly before depopulation, we estimated the week of virus introduction and the length of the period over which the herd emitted virus for each CSFV-infected herd. From these data, we estimated the infection-rate parameter β (the average number of herds infected by one infectious herd during one week) and the herd reproduction ratio, Rh (the average total number of secondary outbreaks caused by one infectious herd, i.e. in its entire infectious period), using a SIR-model for different sets of CSF control measures. When Rh > 1, an epidemic continues to grow. On the other hand, when Rh < 1 an epidemic will fade out.

During the phase before the first outbreak was diagnosed and no specific measures had been implemented, β was estimated at 1.09 and Rh at 6.8. In the subsequent phase infected herds were depopulated, movement restrictions were implemented, infected herds were traced forward and backward and the herds in the protection and surveillance zones were clinically inspected by the veterinary authorities (regional screening). This set of measures significantly reduced β to 0.38. However, Rh was 1.3 and thus still >1. Consequently, the number of outbreaks continued to grow. After a number of additional measures were implemented, the value of Rh was reduced to 0.5 and the epidemic came to an end. These measures included pre-emptive slaughter of herds that had been in contact with infected herds or were located near an infected herd, increased hygienic procedures, replacement of transports of pigs for welfare reasons by killing of young piglets and a breeding ban, and regional screening for CSF-infected herds by local veterinary practitioners.  相似文献   


15.

Background

The Swedish control program for salmonella includes restrictions and on-farm control measures when salmonella is detected in a herd. Required control measures are subsidised by the government. This provides an opportunity to study costs for on-farm salmonella control. The aim of this study was to describe the costs for on-farm salmonella control in Swedish cattle herds and to investigate the effects of herd factors on these costs in dairy herds.

Results

During the 15 years studied there had been a total of 124 restriction periods in 118 cattle herds; 89 dairy herds, 28 specialised fattening herds and three suckler herds. The average costs per herd for on-farm salmonella control was 4.60 million SEK with a median of 1.06 million SEK corresponding to approximately 490 000 and 110 000 EUR. The range was 0.01 to 41 million SEK corresponding to 1080 EUR to 4.44 million EUR per farm. The costs cover measures required in herd-specific control plans, generally measures improving herd hygiene. A mixed linear model was used to investigate associations between herd factors and costs for on-farm salmonella control in dairy herds. Herd size and length of the restriction period were both significantly associated with costs for on-farm control of salmonella with larger herds and longer periods of restrictions leading to higher costs. Serotype detected and administrative changes in the Swedish Board of Agriculture aiming at reducing costs were not associated with costs for on-farm salmonella control.

Conclusions

On-farm control of salmonella in Swedish cattle herds incurred high costs but the costs also varied largely between herds. Larger herds and longer restriction periods increased the costs for on-farm control of salmonella in Swedish dairy herds. This causes concern for future costs for the Swedish salmonella control program as herd sizes are increasing.  相似文献   

16.
A survey of bovine viral diarrhoea virus (BVDV) infection was carried out from June 2001 to July 2002 in a non-vaccinated beef cattle population from the livestock region of Yucatan, Mexico, to assess seroprevalence and identify risk factors related to seroprevalence. The aim was also to estimate the intra-herd correlation (re) and design effect (D) of BVDV seropositivity. Cattle were selected by a two-stage cluster sampling. Blood samples were collected from 560 animals originating from 40 herds. Sera were tested for antibodies against BVDV using an indirect ELISA test. The sensitivity and specificity of the test was 97.9 and 99.7%, respectively. Risk factors regarding the herd and each animal sampled were recorded through a personal interview at the time of blood sampling. Twenty-four of the 40 herds had at least one seropositive animal. The animal true seroprevalence was estimated as 14%. The marginal logistic regression model used to describe the data found a significant (p < 0.05) association of herd size–cow-origin interaction. The interaction was due to a higher risk of seropositivity in the category of herds with ≤100 animals and purchased cows (OR = 1) as compared to herds with ≤100 animals and cows born in the farm (OR = 0.23). Seropositivity between cows purchased and cows born in the farm was similar for herd sizes of 101–196 and >196 animals. The re and D values were 0.17 ± 0.05 and 3.16 ± 0.57, respectively.  相似文献   

17.
We quantified the effect of Neospora caninum (NC)-serostatus on culling and (re)production in 83 herds randomly selected from the Dutch dairy herd population (random group) and in 17 herds that had experienced an abortion epidemic associated with NC infection (epidemic-abortion group). In the random group, a single whole-herd blood sampling was done during the spring of 2003, while in the epidemic-abortion group whole-herd blood sampling was done repeatedly at least once a year starting after the abortion epidemic during the period 1997–2000 until the summer of 2004. Serological test-results for NC were given as ‘negative’ (N), ‘low-positive’ (LP) and ‘high-positive’ (HP). For analysing the time to culling, calving interval and age of first calving, survival analysis was used. For categorical reproduction parameters either a logistic-regression model (abortion, non-return after 1st insemination) or a Poisson-regression model (number of inseminations per pregnancy) was used. For milk production a linear-mixed model was used. All models were controlled, if applicable, for confounding variables like parity, production, season, year and abortion and adjusted for within-herd clustering.

In random herds, HP serostatus increased the hazard for culling 1.73-fold (95% CI: 1.37–2.19) compared to N and LP serostatus. Compared to N serostatus, LP and HP serostatus in epidemic-abortion herds increased the odds for abortion 1.88-fold (95% CI: 1.41–2.52) and 1.72-fold (95% CI: 1.38–2.14), respectively. No other reproduction parameters were associated with NC-serostatus in the random or epidemic-abortion herds. We found no effect of serostatus on milk production in the random group. In contrast, milk production of LP and HP serostatus in the epidemic-abortion group was respectively, 0.72 kg milk/day (95% CI: 0.15–1.03) and 0.59 kg milk/day (95% CI: 0.13–1.30), less during the first 100 days of lactation in the first year after the abortion epidemic compared with N serostatus.  相似文献   


18.
A cross-sectional study was conducted to identify risk factors for herd infection by Brucella spp. in dairy cattle in the suburbs of Asmara, Eritrea. Data were collected from 64 herds, randomly selected from a total of 99 herds with a minimum herd size of 9 cows. A questionnaire was used to gather data on management, hygiene and herd structure. Serum samples collected from all pregnant heifers, cows and bulls, were screened for Brucella infection by the Rose Bengal test (RBT), and all RBT-positive sera re-tested with the complement-fixation test (CFT) for confirmation. A seropositive herd was defined as one in which at least one animal tested positive in the CFT. There were 23 (36%) positive herds among the 64 studied. Both multiple logistic and multiple betabinomial regression modeling were used to analyze the data. Mixed-breed herds, compared to single (exotic)-breed herds, were found to be independently associated with increased herd seroprevalence (OR=5.2, 95% confidence interval 1.4–18.7) in the multiple logistic model with the herd infection status as the dependent variable. The importance of this variable was supported by the multiple betabinomial regression model (OR=3.3, 1.4–7.6) with animal-level prevalence within herd as the outcome variable. Both models also revealed the presence of a negative association between seropositivity and cattle stocking density.  相似文献   

19.
We analysed responses from 147 Fulani herdsmen to a questionnaire about cattle herd-level risk factors for foot-and-mouth disease (FMD) in the previous year. The study used a cross-sectional design with a stratified, two-stage random sample of cattle herds in the Adamawa Province of Cameroon. The questionnaire was pre-tested at a local cattle market before a final version was translated into Foulfoulde (the local Fulani dialect). Variables were screened using a univariable analysis and logistic multiple-regression models were developed in a forward-selection process.

Fifty-eight percent (50–65; 90% CIs) of herdsmen reported FMD in their herd in the previous 12 months. Important risk factors for FMD in the previous 12 months included going on transhumance (OR = 2.6), buying cattle from markets (OR = 2.2), mixing of herds at watering points (OR = 2.4), feeding cotton-seed cake (OR = 3.3), buffalo near the herd (OR = 2.2) and administrative division. For the subset of herds that went on transhumance, coming in contact with an FMDV-diseased herd while on transhumance was the strongest factor (OR = 16).  相似文献   


20.
‘Confidence’ in freedom from disease is generally derived from multiple sources of varied surveillance information, and typically this surveillance evidence has been accumulated over time. In the state of Western Australia (WA) the main surveillance evidence supporting Free Zone status in the national bovine Johne's disease (BJD) program comprises periodic surveys and the ongoing clinical diagnostic system. This paper illustrates a simple approach to current valuation of historical surveillance information, based on the calculated sensitivity of the surveillance processes, the time elapsed since the data were accumulated, and the probability of new introduction of disease into the population during that elapsed time. Surveillance system components (SSCs) contributing to the overall sensitivity of the surveillance system were the clinical diagnostic system and periodic targeted surveys. Sensitivity of each component was estimated using a stochastic scenario tree model of the surveillance process as implemented. Probability of introduction of BJD into WA during each time period was estimated retrospectively from a stochastic import risk analysis model applied to actual cattle importation data. The probability that the WA cattle population was free from infection (at design prevalences of 0.2% of herds and 2% of animals within an infected herd) was estimated following each of 11 years, giving a median probability that the State was free of BJD (at these design prevalences) at the end of 2005 of 0.89. The meaning of this result is discussed.  相似文献   

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