Risk factors for highly pathogenic H7N1 avian influenza virus infection in poultry during the 1999–2000 epidemic in Italy

Risk factors for highly pathogenic H7N1 avian influenza virus infection in poultry during the 1999–2000 epidemic in Italy

Available online at www.sciencedirect.com The Veterinary Journal The Veterinary Journal 181 (2009) 171–177 www.elsevier.com/locate/tvjl Risk factors...

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Available online at www.sciencedirect.com

The Veterinary Journal The Veterinary Journal 181 (2009) 171–177 www.elsevier.com/locate/tvjl

Risk factors for highly pathogenic H7N1 avian influenza virus infection in poultry during the 1999–2000 epidemic in Italy Luca Busani a,b,*, Maria Grazia Valsecchi c, Emanuela Rossi c, Marica Toson a, Nicola Ferre` a, Manuela Dalla Pozza a, Stefano Marangon a a

Istituto Zooprofilattico delle Venezie, viale dell’Universita` 10, 35020 Legnaro, Padova, Italy b Istituto Superiore di Sanita`, viale Regina Elena, 299, 00161 Rome, Italy c Unit of Medical Statistics, Department of Clinical Medicine and Prevention, University of Milano-Bicocca, Via Cadore 48, 20052 Monza, Italy Accepted 13 February 2008

Abstract In 1999–2000, Italian poultry production was disrupted by an H7N1 virus subtype epidemic of highly pathogenic avian influenza (HPAI). The objectives of the present study were to identify risk factors for infection on poultry farms located in regions that had the highest number of outbreaks (Veneto and Lombardia) and the impact of pre-emptive culling as a complementary measure for eradicating infection. A Cox regression model that included spatial factors, such as the G index, was used. The results confirmed the relationship between risk of infection and poultry species, production type and size of farms. The effectiveness of pre-emptive culling was confirmed. An increased risk of infection was observed for poultry farms located near an infected farm and those at altitudes less than 150 m above sea level. The measures for the control and eradication of AI virus infection need to consider species differences in susceptibility, the types of production and the density of poultry farms in the affected areas. Ó 2008 Elsevier Ltd. All rights reserved. Keywords: Avian influenza; Poultry; Epidemiology; Survival analysis; Risk factors

Introduction In 1999–2000, Italy experienced an epidemic of highly pathogenic avian influenza (HPAI) in industrial poultry population. The epidemic was caused by an H7N1 subtype, which had been circulating in the area as a low pathogenicity avian influenza (LPAI) virus since March 1999 and began to spread rapidly in December 1999, after having mutated into HPAI virus (Capua and Marangon, 2000). The evolution of LPAI viruses of the H5 and H7 subtypes circulating in a domestic poultry population has been described in other countries, such as the United States (Pennsylvania) and Mexico (Bean et al., 1985; Garcia et al., 1996). * Corresponding author. Address: Istituto Zooprofilattico delle Venezie, viale dell’Universita` 10, 35020 Legnaro, Padova, Italy. Tel.: +39 049 8084332; fax: +39 049 8830268. E-mail address: [email protected] (L. Busani).

1090-0233/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.tvjl.2008.02.013

To contain the epidemic and eradicate infection, all measures provided for by EU legislation were applied from 17th December 1999, including culling at infected premises (IP), prohibiting the restocking of poultry farms and restricting the movement of live poultry, vehicles and personnel in the areas at risk (CEC, 1992). Moreover, preemptive culling was carried out on poultry farms located near an IP, those that had at risk contacts with an IP and those that belonged to the owner as the IP. Furthermore, to monitor infection in the affected regions, intensive surveillance was implemented. Despite these eradication measures, the infection spread to 413 poultry farms; as a result, approximately 16 million birds died or were culled in infected or at risk farms and an estimated 110 million Euros in compensation were paid to farmers (Marangon et al., 2005). The areas most affected by the epidemic were the regions of Lombardia and Veneto in North-Eastern Italy, where 382/413 (92.5%) outbreaks

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occurred and where around 65% of the Italian poultry production is concentrated (Mannelli et al., 2006). AI viruses are not airborne and their introduction in poultry farms mainly occurs through direct or indirect contact with infected birds, resulting from the movement of live poultry, people, vehicles, equipment or contaminated materials (Stegeman et al., 2004; Marangon et al., 2005; Capua and Marangon, 2006). Moreover, in a study of the HPAI H7N7 epidemic that occurred in the Netherlands in 2003, poultry species and type of poultry production were shown to have key roles in the dissemination of AI virus (Thomas et al., 2005). However, in that study, the evaluation of the risk factors for AI did not take into account the time of infection at the farm level or the exposure time for each farm at risk. The objective of the present study was to quantify risk factors for AI virus infection in the 1999–2000 Italian epidemic, taking into account the time of infection and the exposure time at farm level. We also assessed the impact of pre-emptive culling as a complementary measure for eradicating infection. Materials and methods Study design The study area consisted of parts of the Veneto and Lombardia regions where the greatest number of infections occurred during the epidemic (Fig. 1). The study period began on 28th November 1999 (i.e., the day that HPAI virus was first suspected of having infected a poultry farm in the study area; day 0) and it ended on 31st March 2000 (the day that the last outbreak was identified; day 125).

All 3122 industrial poultry farms located in the study area during the study period were considered in the analysis, including the 382 farms involved in the epidemic (Table 1). During the study period, there were 4251 production cycles, the duration of which were different by poultry species and type of production. We did not include commercial farms that were not active during the study period or backyard poultry farms in the analysis. Veneto had 64.1% of the farms, 65.2% of the production cycles and 39.8% of the farms involved in the epidemic. In both regions, broiler production was the most common type of poultry production, accounting for 39.6% of the farms and 50.8% of the production cycles. Each farm was involved in only one type of poultry production. In Lombardia, 21.9% of farms were laying-hen farms, which represented 16.9% of the total production cycles in the region; in Veneto, the corresponding percentages were 7.0% and 5.0%, respectively. Meat-turkey production was more common in Veneto (28.1% of farms and 22.9% of production cycles), compared to Lombardia (15.0% of farms and 12.7% of production cycles). Data on species and production type, size of the farm (number of birds per production cycle), precise duration of each production cycle and geographical location were collected for all of the poultry farms by veterinarians working for the Regional Veterinary Services. In all IPs, epidemiological investigations were conducted to determine the possible origin of infection and to identify farms that were in direct or indirect contact with infected farms, by interviewing farmers using a standardised questionnaire. The questionnaire also included information on the date of onset of clinical signs and the date that infection was confirmed for all IPs. As potential risk factors for infection, we considered poultry species, production type, size of farm, altitude of farm and distance between farm and the nearest infected or potentially infectious farm. Potentially infectious farms were defined based on a temporal risk window (TRW) (Taylor et al., 2004). The beginning of the TRW was estimated as follows: (1) for laying hens and quails: date of onset of clinical signs [integer(0.5 + 14 days + 2*n1)]; (2) for other species: date of onset of clinical signs [integer(0.5 + 4 days + 2*n2)]. The end of the TRW was considered to be the date of outbreak extinction (culling of all birds and disinfection of poultry premises). The two parameters n1 and n2 were random values between 0 and 12 and between 0 and 10, respectively.

Fig. 1. 1999–2000 H7N1 HPAI epidemic in Italy: Geographical distribution of infected farms in the Lombardia and Veneto regions.

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Table 1 1999–2000 H7N1 Highly pathogenic avian influenza in Italy: distribution of the number of farms, production cycles and outbreaks by species and type of production in the Veneto and Lombardia regions

autocorrelation index Gi ranged from 28.9 to 84.6 (mean 55.4, median 57.5).

Species

Statistical analysis

Lombardia region Number % of farms

Broiler Layers Broiler breeders Turkey meat Turkey breeders Other species* Total Veneto region Broiler Layers Broiler breeders Turkey meat Turkey breeders Other species* Total

*

Number of % outbreaks

360 246 81 168 4

32.1 21.9 7.2 15.0 0.4

654 250 83 187 4

44.2 16.9 5.6 12.7 0.3

23 96 21 72 3

10.0 41.7 9.1 31.3 1.3

262

23.4

300

20.3

15

6.5

1121

100.0 1478

100.0 230

100.0

875 140 74 563 47

43.7 1506 7.0 140 3.7 79 28.1 635 2.3 56

54.3 11 5.0 20 2.8 8 22.9 103 2.0 2

7.2 13.2 5.3 67.8 1.3

302

15.1

12.9

2001

Total Broiler 1235 Layers 386 Broiler breeders 155 Turkey meat 731 Turkey 51 breeders 564 Other species* Total

Number of % production cycles

3122

8

5.3

100.0 2773

100.0 152

100.0

39.6 2160 12.4 390 5.0 162 23.4 822 1.6 60

50.8 34 9.2 116 3.8 29 19.3 175 1.4 5

8.9 30.4 7.6 45.8 1.3

18.1

357

657

100.0 4251

23

6.0

100.0 382

15.5

100.0

Includes geese, quail, ostriches, guinea fowl and pheasants.

The date of infection was defined as the date that the virus was introduced to the farm, and was considered to have occurred 7 days before the detection of clinical signs; this time period was established by taking into consideration simulations based on published data and field observations (Van der Goot et al., 2003; Marangon et al., 2005). The effect of pre-emptive culling at farms located within 1 km of an IP on the probability of AI virus infection was estimated by comparing the probability before and after implementation of this measure (begun on 19th January 2000; day 52). Because pre-emptive culling was performed on more farms and in a more timely manner in Veneto compared to Lombardia, the two regions were compared by creating two variables to take into account if a farm was operational before or after day 52 and if it was located in Veneto or Lombardy.

Geographical clustering of IPs Clustering of IPs was expressed using the G statistic, which is a measure of the local spatial autocorrelation of IPs, weighted by the distance between the IPs (Getis and Ord, 1992; Ord and Getis, 1995). The autocorrelation index for each IP was calculated as follows: PN j xj wji ; i–j G i ¼ PN j xj where xj = 1 for the IP and = 0 for non-infected farms and wji is the reciprocal of the square root of the distance between a farm (i) and the IP. The

Poultry farms were the units used for the statistical analyses. Depending on the type of production cycle (all in-all out or continuous) and the poultry species reared, farms were not necessarily exposed to infection continuously. Field exposure was determined by the time in days during which each farm was in operation. Observations began on the date of first restocking after 28th November 1999 (truncated time) or, if the farm had been restocked prior to this date, on 28th November 1999. Observations ended on the estimated date of virus introduction or, in any case, on 31st March 2000. The evolution of the epidemic was described by estimating the probability of virus introduction over time. The risk of infection as a function of the considered risk factors was modelled using the marginal Cox regression model, in which the time-dependent exposure (contact with an IP) and the presence of a time-dependent covariate (distance from an IP) were managed by expanding the dataset to a total of 233,450 records (Andersen and Gill, 1982; Therneau and Grambsch, 2000). The time-cumulative probability of a farm becoming infected was estimated according to Kaplan–Meier, with standard error calculated according to Greenwood; the log-rank test was used to compare the history of infection between different groups, as defined by each risk factor, for non-time-dependent variables, whereas the Mantel–Byar test was used for the time-dependent risk factor (distance from the nearest IP) (Marubini and Valsecchi, 1995). Continuous variables were categorised according to both accepted standards and the functional form suggested by interpolation with the lowest smoother of the Martingale residuals of the Cox model fitted on all continuous and categorical variables of interest. In this way, categories for distance between farms were defined according to accepted standards as: <1500, 1500–3000, 3000–4500 and P4500 m (Stegeman et al., 2004; Taylor et al., 2004; Mannelli et al., 2006). The three categories for altitude above sea level (asl) were defined on the basis of residuals (640, 40–150 and P150 m). Residual analyses suggested a cut-off value of 60 for the Gi index and a 10,000 bird cut-off for farm size (included in the model in the logarithmic scale due to its skewness). Additional categories above the cutoff (610,000 birds; 10,000–30,000 birds; 30,000–50,000 birds, >50,000 birds) were defined to better describe possible trends in risk according to farm size. First-order interactions between paired risk factors were analysed; none were significant. The proportional hazard assumption was graphically checked for each covariate by plotting the logarithm of the nonparametric estimate of the cumulative hazard against time. Only the G statistic suggested that there were major deviations; thus the final Cox model was stratified for the two categories of the Gi index and included the dummy variables for all other factors in the regressor. The stratification of the Cox regression model for the defined Gi index (P60 and <60) allowed the model to be adjusted for effects related to the local distribution of IPs and unaccounted for by the distance between farms. The Wald test was used to assess the impact of each factor on the time to infection and estimates of the hazard ratio (HR) with the related 95% confidence intervals (95% CI) were given. Data analysis was performed using SAS statistics software (Version 8.2; SAS Institute) and the analyses were conducted using the R (version 1.9.0; http://CRAN.R-project.org) coxph function.

Results Univariate analysis of risk factors The overall cumulative probability of farms being infected was 17.0% (95% CI: 15.4–18.6) at the end of the

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study period (i.e., 125 days after the occurrence of the first outbreak). The probability increased from day 20 (1.6%,

95% CI: 1.1–2.1) to day 70 (14.4%, 95% CI: 13.0–15.8), which was the period with the highest number of cases of

Fig. 2. 1999–2000 H7N1 HPAI epidemic in Italy: Kaplan–Meier plot of the probability of AI virus infection at farm level for the considered risk factors.

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HPAI epidemic in the study area (Fig. 2A). After day 70, the probability of infection reached a plateau. The cumulative probability of infection by risk factor is shown in Fig. 2B–F and the point estimates are provided in Table 2, with 95% CI. Lombardia had a significantly higher cumulative probability of infection than Veneto (Fig. 2B). For both regions, the incidence curve appeared to flatten after pre-emptive culling was initiated, but the risk of infection at the end of the study period was lower in Veneto. Considering type of poultry production and species, the probability of infection was highest for meat turkeys and laying hens, followed by breeders (turkeys and broilers considered together), whereas it was lowest for broilers and other poultry species (Fig. 2C). The probability of infection was also significantly higher for farms located at 6150 m asl compared with farms located P150 m asl (Fig. 2D).

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With regard to farm size, the cumulative probability of infection ranged from 8.2% for farms with 610,000 birds to 29.4% for farms with >50,000 birds (Fig. 2E). The probability of infection was inversely related to the distance from an IP: it ranged from 66.0% for farms within 1500 m of an IP to 9.6% for those more than 4500 m away from an IP (Fig. 2F). Multivariate analysis of risk factors The results of the multivariate analysis are shown in Table 3. When comparing Lombardia and Veneto, the risk of infection was comparable before pre-emptive culling (HR: 0.80; 95% CI: 0.59–1.09), whereas after pre-emptive culling the risk of infection in Veneto was approximately one third that in Lombardia.

Table 2 Farms at risk of AI virus infection, infected farms and cumulative probability of infection at the end of the study period, calculated for each risk factor during the 1999–2000 HPAI H7N1 epidemic in Italy Variables Region Bird type

Altitude Farm size (Number of birds)

Distance from nearest Outbreaka

a

Veneto Lombardia Broilers Meat turkeys Laying hens Breeders Other species 6150 m >150 m <10,000 10,000–30,000 30,000–50,000 >50,000 <1.5 km 1.5–3 km 3–4.5 km >4.5 km

Number of farms

Number of infected farms

Cumulative probability of infection %

95% confidence interval

Log rank test

P-value

2001 1121 1247 732 383 202 558 2495 627 896 1377 452 397 – – – –

152 230 34 175 116 34 23 361 21 58 172 68 84 60 70 74 178

11.0 25.3 4.9 35.3 31.2 19.2 4.9 20.5 4.4 8.2 18.3 22.2 29.4 66.0 63.2 42.1 9.6

9.312.7 22.528.1 3.36.5 30.839.8 26.535.9 13.425.0 2.96.9 18.622.4 2.56.3 6.210.2 15.820.8 17.427.0 24.034.8 54.177.9 44.981.5 33.750.5 8.810.4

228.12

<0.0001

311.92

<0.0001

70.43

<0.0001

71.10

<0.0001

428.39

<0.0001

Due to the time-dependency of this variable, it was not possible to calculate the number of farms.

Table 3 1999–2000 H7N1 highly pathogenic avian influenza in Italy: results of the Cox’s regression model for the estimation of the hazard of infection at farm level for the different risk factors (3122 farms as reference population, 382 events) Variables

Regression coefficient

P-value

Hazard ratio eb

95% Hazard ratio confidence interval

Veneto before 19/01/2000 vs. Lombardia Veneto after 19/01/2000 vs. Lombardia Altitude 640 m vs. >150 m Altitude 40–150 m vs. >150 m 10,000–30,000 birds vs. <10,000 30,000–50,000 birds vs. <10,000 P50,000 birds vs. <10,000 Meat turkeys vs. Broilers Laying hens vs. Broilers Breeders vs. Broilers Other vs. Broilers D 1500 vs. >4500 D 3000 vs. >4500 D 4500 vs. >4500

0.22 1.08 0.83 1.20 0.35 0.93 1.18 2.41 1.92 1.83 0.39 1.52 1.19 1.11

0.16 <0.0001 0.0008 <0.0001 0.031 <0.0001 <0.0001 <0.0001 <0.0001 <0.0001 0.15 <0.0001 <0.0001 <0.0001

0.81 0.34 2.30 3.32 1.42 2.54 3.27 11.10 6.83 6.23 1.48 4.55 3.29 3.03

0.601.09 0.220.51 1.413.72 2.125.22 1.031.94 1.743.70 2.254.74 7.6616.11 4.6110.11 3.8110.20 0.872.51 3.156.56 2.364.59 2.214.15

Likelihood ratio test = 515; P < 0.0001; Degrees of freedom = 14; D = Distance from nearest outbreak.

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All other factors considered in the univariate analysis remained significantly associated with infection in the multivariate analysis. Compared to poultry farms located at altitudes P150 m asl, those at 640 m asl showed a twofold risk of infection and those at 40–150 m asl showed a threefold risk. With regard to species and type of production, the risk of infection was greatest for meat turkey farms, compared to the other types of production, although only 9.4% of the meat turkey farms had >30,000 birds. Both laying hens and breeders had a six-fold risk of infection compared to broilers; 46.7% of laying hen farms had >30,000 birds, whereas only 5.3% of breeder farms had >30,000 birds. Regardless of production type, the risk increased with size and farms with >30,000 birds had a 2–3 times greater risk than those with <10,000 birds. Proximity to an IP during the TRW was also shown to be a significant risk factor. Compared to farms located P4500 m away from an IP, both those 1500–3000 m and those within 3000–4500 had an approximately three times greater risk of infection, whereas those within 1500 m had a 4–5 times greater risk. Discussion The results of this study confirmed that poultry species, type of production and farm size were risk factors for HPAI infection in the epidemic in North-Eastern Italy (Mannelli et al., 2006). They also showed that pre-emptive culling, greater distance from infected farms and higher altitudes all had a protective effect. Our finding of an association of AI virus infection with poultry species is consistent with previous reports of species differences in susceptibility to both low and high pathogenicity viruses (Perkins and Swayne, 2003; Tumpey et al., 2004). Previous studies have also shown that turkeys are more susceptible to infection than chickens (Mutinelli et al., 2003; Tumpey et al., 2004). The association between risk of infection and type of poultry production is also consistent with data from the HPAI epidemic in the Netherlands (Thomas et al., 2005). Production cycles are longer for meat turkeys, layers and breeders than broilers; in Italy, the average length of the production cycle is about 90–100 days for female turkeys and 130–140 days for male turkeys; layers and breeders have a cycle of up to two years and broilers have an average cycle of 46 days. In our survival analysis, we considered only the actual duration of the production cycle as the time at risk. The importance of considering this duration lies in the fact that it differs by species and production type and that these factors can influence the risk of infection. Our model also took into account the point in time pre-emptive culling was initiated and the duration of culling. With regard to farm size, the results of this analysis confirm those of our previous study on the H7N1 HPAI epidemic in Italy (Mannelli et al., 2006). In the previous study, only two categories of farm size were considered,

whereas in the present study we defined four categories and showed that the risk of infection progressively increased with farm size. One explanation might be that, on larger farms, there is a higher number of at risk contacts because of the more frequent movement of feed trucks and the presence of additional temporary staff, especially during specific phases of the production cycle (e.g., debeaking, vaccine administration, individual drug treatment and loading for slaughter). The risk of AI virus infection increased with proximity to an IP during its infectious period (TRW). Many routes of AI virus transmission among flocks have been proposed, including ‘neighbourhood’ (‘contiguous’) spread, which refers to the short-distance transmission from an IP to a previously uninfected farm through unknown factors (Henzler et al., 2003). Previous studies on the Italian HPAI epidemic also evaluated ‘neighbourhood spread’ and reported some ‘hot spots’, which are areas where there is a high clustering of cases (Mannelli et al., 2006; Mulatti et al., 2007). These results confirm the role played by farm density in the spread of AI viruses. The role of farm density was also supported by the effects of pre-emptive culling, a measure that reduced the density of susceptible poultry farms, mainly around the IP, thus also reducing the related risk of infection. The observed neighbourhood spread may also have been influenced by the flow of people and vehicles. Although we collected this information for all IPs and for a subset of uninfected poultry farms in the area, we did not include it in our analysis because the data were of poor quality. Given that indirect contact between farms is one of the most important routes for the spread of HPAI virus in a densely populated poultry area (DPPA), lack of this information may have had an important effect on our results (Stegeman et al., 2004; Marangon et al., 2005; Capua and Marangon, 2006). With regard to pre-emptive culling, although a reduction in the risk of infection was observed in both regions following the implementation of this measure, the reduction was only significant in Veneto. Mannelli et al. (2007) showed that the reproductive ratio of HPAI (the average number of new IPs caused by an IP) was lower in Veneto, particularly in the latter stages of the epidemic. In Veneto, pre-emptive culling was started earlier and on a higher number of farms (68 farms) than in Lombardia (12 farms). The extent of pre-emptive culling for containing and eventually eradicating an HPAI epidemic in a DPPA must be considerable and the culling radius around the IP and the timeliness of implementation are critical parameters. Preemptive culling was also shown to be effective in the 2003 HPAI epidemic in the Netherlands (Stegeman et al., 2004; Boender et al., 2007). The finding that the risk of infection was lower in farms located in hilly areas (P150 m asl), compared to those at lower altitudes, could be explained by the fact that contact between farms is more difficult in hilly areas. Other unknown factors, such as local environmental or climatic conditions, may also have influenced the risk of infection.

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Conclusions The results of our study demonstrate the importance of using statistical methods that take into account time at risk for individual farms in a DPPA when evaluating AI risk factors. The results also show that the planning of measures for the control and eradication of infection need to consider species differences in susceptibility, the types of production and the density of poultry farms in the affected areas. Although pre-emptive culling was not implemented immediately after the epidemic in Italy began, its application in poultry farms at risk for AI proved to be effective. The results indicate that reduction of effective farm density and prompt implementation of biosecurity, stamping out, restrictions and pre-emptive culling are effective measures for preventing and controlling HPAI infection in a DPPA. Conflict of interest statement None of the authors of this paper has a financial or personal relationship with other people or organisations that could inappropriately influence or bias the content of the paper . Acknowledgements This work was supported by the grant FP6-513737 from the EU Commission and by a grant from the Italian Ministry of Health for the control of avian influenza in Italy. References Andersen, P.K., Gill, R.D., 1982. Cox’s regression model for counting processes: a large sample study. Annals of Statistics 10, 1100–1120. Bean, W.J., Kawaoka, Y., Wood, J.M., Pearson, J.E., Webster, R.G., 1985. Characterization of virulent and avirulent A/chicken/Pennsylvania/83 influenza A viruses: potential role of defective interfering RNAs in nature. Journal of Virology 54, 151–160. Boender, G.J., Hagenaars, T.J., Bouma, A., Nodelijk, G., Elbers, A.R., de Jong, M.C., van Boven, M., 2007. Risk maps for the spread of highly pathogenic avian influenza in poultry. PLoS Computational Biology 3, e71. doi:10.1371/journal.pcbi.003007. Capua, I., Marangon, S., 2006. Control of avian influenza in poultry. Emerging Infectious Diseases 12, 1319–1324. Capua, I., Marangon, S., 2000. Avian influenza in Italy (1999–2000): a review. Avian Pathology 29, 289–294. CEC, 1992. Council Directive 92/40/EEC of 19 May 1992 introducing Community measures for the control of avian influenza. Official Journal of the European Commission L167, 1–15. Garcia, M., Crawford, J.M., Latimer, J.W., Rivera-Cruz, E., Perdue, M.L., 1996. Heterogeneity in the haemagglutinin gene and emergence of the highly pathogenic phenotype among recent H5N2 avian influenza viruses from Mexico. Journal of General Virology 77, 1493–1504. Getis, A., Ord, J.K., 1992. The analysis of spatial association by use of distance statistics. Geographical Analysis 24, 189–206.

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