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Brief Communication |
Correspondence: 1 Corresponding Author: Dominique J Bicout, Biomathematics and Epidemiology Unit TIMC, National Veterinary School of Lyon, 1 avenue Bourgelat, B.P. 83, 69280 Marcy l'Etoile, France, bicout{at}ill.fr
| Abstract |
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0.5%, 26 with 0.5% < P
1.5%, 10 with 1.5% < P
5%, and 4 with 5% < P
25%.
Key Words: Brazil equine infectious anemia virus prevalence relative risk
| Introduction |
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Equine infectious anemia virus is distributed worldwide and exists in an enzootic form in about 23% of countries. In Brazil, the first confirmed EIA case was reported in Minas Gerais State (MGS) in 1968,2 and the AGID has been used as the official diagnostic test for EIA since 1974. In 1998, 131,991 horses out of 8,391,942 were tested in all Brazil for EIA, and 3,689 of them were classified as positives, resulting in a prevalence of 3%. According to the local office of the Brazilian Ministry of Agriculture, the EIA prevalence in MGS was 0.88% from 1973 to 1991 and 0.69% from 1995 to 2001, whereas it was about 25% in the Pantanal, the largest swamp area in Brazil.7 The EIA status remains unknown for most (about 98%) horses in Brazil (Boletim de Defesa Agropecuária, Anemia Infecciosa Eqüina, Brasilia, DF, 1998) because the AGID tests conducted by accredited laboratories are performed only for horse transportations (interstate and international trades) and horse shows. Therefore, a quantitative risk assessment of EIA could be very informative and useful for decision makers and horse industries.
The main objective of the study reported here was to provide a city-level distribution of EIA prevalence in the north of MGS, based upon a comprehensive analysis of raw data from AGID test results collected between January 2002 and December 2004.
The northern region (NR) of MGS is situated in the southeast of Brazil, between latitudes 14°13'57''S and 22°55'22''S and longitudes 39°51'23''W and 51°02'45''W. The NR, with an area of 126,521 km2 (22% of the MGS), is composed of 89 municipalities or cities and includes about 19% of the MGS horse population (211,636 horses).a It is geographically divided into 3 river basins: São Francisco River (SFR), Pardo River (PR) and Jequitinhonha River (JR), which cover 80%, 10.5%, and 9.5%, respectively, of the total area. The dominant ecosystem is the tropical savannah or Cerrado, the yearly temperatures average between 21°C and 24°C with temperatures greater than 24°C in the rainy season, and the average annual rainfall is between 1,000 mm and 1,500 mm.a
From January 2002 to December 2004, a total of 8,981 AGID tests were conducted by the Animal Surveillance Service of Minas Gerais, 37% of which were performed during the rainy season (from October to March) and 63% during the dry season. A total of 284 horses were found to be positive for EIA (AGID-positive), 2.9% of positive horses during the rainy season and 2.7% positives in the dry season. As summarized in Table 1, all the samples tested originated from 68 cities, while the remaining 21 cities (accounting for 13% of the horse population) contributed no samples. The distribution of samples according to river basins was: 5,108 (57%) from SFR, 200 (2%) from PR basins, and 3,673 (41%) from JR basin. The distribution of the positive horses was 279 (98.2%) from SFR, 2 (0.7%) from PR, and 3 (1.1%) from JR.
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1. Step 1: Spatial Interpolation
From the total N = 89 cities in the NR, just a single test was reported for each of 2 cities and no test from 21 cities during the 3-year study period (January 2002 to December 2004) (Table 1). In order to generate the subset of missing data for those 23 cities (Kj, where j = 1,2,...,23), the initial number of positives per city that were available (Ki, where i = 24,25,...,N) were transformed into rescaled data as,
. The Yi (see Appendix) and their associated spatial coordinates xi,yi of the centroids of each city (plus those of missing data) were used in the spatial prediction model as implemented in GeoBUGS (a module of WinBUGSb) to produce the interpolated Yj and thus the interpolated number of positives, Kj. About 5,000 iterations were used for the convergence of the interpolation process. The new set of the number of positives (reported plus the interpolated ones) were denoted as K i in the subsequent step.
2. Step 2: Estimated Relative Risk and Prevalence Calculations
The number of positives i for i = 1,2,...,N, the number of expected positives
under the homogeneous hypothesis, and the matrix A of adjacent neighbors (Aij = 1 for cities i and j sharing a common border and Aij = 0 otherwise) were used in a log linear model (see Appendix). For each city, the model incorporates both spatial correlations and unstructured variability. The software WinBUGSb was used for Markov chain Monte Carlo simulations to find Bayesian estimates of the model parameters and calculate the estimated relative risk RRi for each city (see Appendix). About 100,000 iterations were used for equilibration of the process. Subsequently, the prevalence for each city was simply obtained from the relation, Pi = Ei x RRi/Si.
The results of the 2-step calculations are presented in Table 1 and the estimated prevalence distribution on the map in Figure 1. In Table 1, the distribution of EIAV prevalence (P) is considered at the level of river basins and sorted into 4 classes of increasing prevalence according to the legend in Figure 1: null (0 < P
0.5%), low (0.5% < P
1.5%), medium (1.5% < P
5%), and high (5% < P
25%). The number of cities classified with P
0.5% were 40 (45% of the cities in NR), distributed as 29 (33%) in SFR, 6 (7%) in PR, and 5 (6%) in JR, and corresponding to 31% of farms (average size, 188 ha vs. 120 ha for P < 0.5%) and 48% of the horse population. The number of cities with no reported EIA tests was 4 in the null class of prevalence, 14 in low, 3 in medium, and zero in high classes.
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0.5%. These cities contain 34% of NR active agricultural workers; are characterized by high horse and bovine population densities (Table 1); produce 36% of the beef and 50% of the milk, respectively, for Brazil; occupy 44% of the rural area; and stretch all around and along the major rivers SFR and PR (Fig. 1).
Rather unexpectedly for a subtropical region like NR, no significant difference (
2 test P value > 0.05) was found in the proportion of EIA positives between the rainy and dry seasons. Indeed, because of the subclinical nature of EIA infection it was impossible to accurately time the infection onset, and therefore to study any correlations between the seasonality and the potential risk of EIA virus transmission and spreading by insects as documented in the literature.1 On the other hand, the increase by a factor of 1.7 in the number of tests during the dry season seems to be correlated with an increase in horse events like horse shows and races from March to September, as revealed by inspection of event schedules for 5 horse breeding associations.
The EIA relative risk and prevalence map generated in this study is informative and useful to surveillance programs for intra- and interstate horse transportations, as it indicates areas and cities where control barriers could be reinforced. However, improving our knowledge on the spread and persistence of EIA infection and finding more effective methods to deal with likely outbreaks would require combination of modeling and further investigations, including longitudinal studies on antibody kinetics and establishment of long-term asymptomatic infection.3
| Appendix |
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s.e(µi, xi, yi,
,
,
), where µi = ß is the mean of log(Yi) of each city, (xi,yi) spatial coordinates of the centroids of each city,
a scalar representing the precision of the model, and
and
are parameters of the covariance, exp{(
dij)k}, with dij the interpoint distance between cities "i" and "j." The parameters ß,
,
and
used for the kriging were chosen as follows: ß
dflat() (is a random variable from the whole real line),
dgamma(0.1,0.001) (is Gamma distributed random variable of exponent 0.1 and argument 0.001),
dunif(0.001,0.8) (is a uniform distributed random variable from the interval [0.001,0.8]), and
dunif(0.05,1.95) (is a uniform distributed random variable from the interval [0.05,1.95])., The mean values after 5,000 iterations were: ß = 0.718,
= 0.052,
= 0.407, and
= 0.092.
s.up(ß, xj, yj, log(Yi)), where (xi,yj) are spatial coordinates associated to the Yj.
Relative Risk Estimation. The number of positives i in each city is assumed to follow a Poisson distributions of parameters or means µi (i.e., i. Poisson(µi)) and the unknown relative risk RRi are defined as, RRi = µi/Ei, where Ei are the expected number of positives as defined in the text. And the estimated prevalence Pi for each city is obtained as the ratio of the estimated number of positives µi to the population Si of the city, i.e., Pi = µi/Si = Ei x RRi/Si. To determine the µis, we used the log-linear model for the relative risk as, log(RRi) = log(µi) log(Ei) =
+ ui + vi, which takes into account the overall random effect
of the relative risk and the correlated ui and uncorrelated vi heterogeneities. The parameters were chosen as follows:
dflat() (is a random variable from the whole real line) and the uncorrelated random heterogeneity vi
dnorm(0,tau.v) (is a Gaussian distributed random variable of mean zero and inverse-variance tau.v) with tau.v
dgamma(0.1,0.001) (a Gamma distributed random variable of exponent 0.1 and argument 0.001). For the spatial correlated heterogeneity ui, we used the clustering structure where the risk in any city depends on neighboring cities as described in the CAR model in GeoBUGS, ui
car.normal(A), where A is the matrix of adjacent neighbors (see the text). The mean values after 100,000 iterations were:
= 3.20, tau.v = 22.56.
| Acknowledgments |
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| Sources and manufacturers |
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a Data available from Instituto Brasileiro de Geografia e Estatistica (IBGE): http://www.ibge.gov.br. ![]()
b WinBUGS v1.4, Imperial College and Medical Research Council, London, UK. ![]()
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