Transmission of classical swine fever virus within herds during the 1997–1998 epidemic in The Netherlands

Preventive Veterinary Medicine 42 (1999) 201±218

Transmission of classical swine fever virus within herds during the 1997±1998 epidemic in The Netherlands Arjan Stegemana,*, Armin R.W. Elbersb, Annemarie Boumac, Hans de Smitc, Mart C.M. de Jonga a

Department of Immunology, Pathobiology and Epidemiology, Institute for Animal Science and Health, PO Box 65, 8200 AB Lelystad, The Netherlands b Department of Pig Health, Animal Health Service, PO Box 4, 5280 AA Boxtel, The Netherlands c Department of Mammalian Virology, Institute for Animal Science and Health, PO Box 65, 8200 AB Lelystad, The Netherlands Accepted 20 June 1999

Abstract In this paper, we describe the transmission of Classical Swine Fever virus (CSF virus) within herds during the 1997±1998 epidemic in the Netherlands. In seven herds where the infection started among individually housed breeding stock, all breeding pigs had been tested for antibodies to CSF virus shortly before depopulation. Based upon these data, the transmission of CSF virus between pigs was described as exponential growth in time with a parameter r, that was estimated at 0.108 (95% confidence interval (95% CI) 0.060±0.156). The accompanying per-generation transmission (expressed as the basic reproduction ratio, R0) was estimated at 2.9. Based upon this characterisation, a calculation method was derived with which serological findings at depopulation can be used to calculate the period in which the virus was with a certain probability introduced into that breeding stock. This model was used to estimate the period when the virus had been introduced into 34 herds where the infection started in the breeding section. Of these herds, only a single contact with a herd previously infected had been traced. However, in contrast with the seven previously mentioned herds, only a sample of the breeding pigs had been tested before depopulation (as was the common procedure during the epidemic). The observed number of days between the single contact with an infected herd and the day of sampling of these 34 herds fitted well in the model. Thus, we concluded that the model and transmission parameter was in agreement with the transmission between breeding pigs in these herds. Because of the limited sample size and because it was usually unknown in which specific pen the infection started, we were unable to estimate transmission parameters for weaned piglets and *

Corresponding author. Tel.: ‡31-320-238-238; fax: ‡31-320-238-050 E-mail address: [email protected] (A. Stegeman) 0167-5877/99/$ ± see front matter # 1999 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 7 - 5 8 7 7 ( 9 9 ) 0 0 0 7 6 - 8

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finishing pigs from the data collected during the epidemic. However, from the results of controlled experiments in which R0 was estimated as 81 between weaned piglets and 14 between heavy finishing pigs (Laevens et al., 1998a. Vet. Quart. 20, 41±45; Laevens et al., 1999. Ph.D. Thesis), we constructed a simple model to describe the transmission of CSF virus in compartments (rooms) housing finishing pigs and weaned piglets. From the number of pens per compartment, the number of pigs per pen, the numbers of pigs tested for antibodies to CSF virus and the distribution of the seropositive pigs in the compartment, this model gives again a period in which the virus most probably entered the herd. Using the findings in 41 herds where the infection started in the section of the finishers or weaned piglets of the age of 8 weeks or older, and of which only a single contact with a herd previously infected was known, there was no reason to reject the model. Thus, we concluded that the transmission between weaned piglets and finishing pigs during the epidemic was not significantly different from the transmission observed in the experiments. # 1999 Elsevier Science B.V. All rights reserved. Keywords: Classical Swine Fever; Transmission; Within-herd; Breeding pigs; Weaned piglets; Finishing pigs; Model

1. Introduction Although Classical Swine Fever (CSF) is a very important disease, few publications report quantitative estimates of the transmission of CSF virus between pigs. Recently, Laevens et al. (1998a), (1999) reported experimental quantification of the transmission of CSF virus. However, to our knowledge, estimates of the transmission of CSF virus from natural outbreaks in commercial pig herds have not been reported. The reason for this may be that the control strategy in large parts of the world includes depopulation of infected herds as soon as possible. This stamping-out strategy hampers measuring withinherd transmission and also directs the epidemiological analysis of outbreaks towards the investigation of contacts that can transmit CSF virus between-herds. Another reason, however, might be that methods to quantify the transmission between animals have become common knowledge only recently (de Jong, 1995). However, even in countries that apply a stamping out policy to control CSF, quantitative knowledge of the within-herd transmission of the virus is important. This is because the transmission of a pathogen within a herd has a great influence on the transmission of that pathogen between-herds (Van Nes et al., 1998). Quantitative knowledge of the transmission of CSF virus will be of great help in the design of programmes to rapidly detect infected herds. The reason for this is that the combination of the sample size, the sensitivity of the tests (including clinical diagnosis) and the sampling interval on the one hand and the within-herd transmission of the virus on the other hand, both determine the average period between introduction of CSF virus and detection of CSF. Thus, both determine the amount of viral exposure. In addition, during epidemics, transmission parameters are useful to estimate the period when CSF virus was most-likely introduced into CSF-infected herds. This is especially important during large epidemics, when there is limited manpower in relation to the huge number of contact herds to be visited. Narrowing of the suspected infectious periods is then of great help to

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the veterinary authorities to restrict the number of herds included in the forward and backward tracing. Laevens et al. (1998a, 1999) experimentally quantified the transmission of CSF virus in weaned piglets and slaughter pigs. The basic reproduction ratio (R0, the average number of secondary cases caused by one infectious individual) was estimated as 81 within a pen of weaned piglets and as 14 within a pen of slaughter pigs. They also described the time that elapsed before pigs in two adjacent pens became viremic. From this experiment, they designed a model to estimate the day of virus introduction in natural outbreaks from serological data of the pen with the highest seroprevalence (Laevens et al., 1998b). The model fitted well on the data that had been collected in 3 herds infected during the CSF epidemic in Belgium in 1993±1994. To use this model, however, it is necessary to test all pigs in a herd. During a large epidemic Ð like the one we had in the Netherlands in 1997±1998 (Elbers et al., 1999) Ð this is often in conflict with the strategy that infected herds are to be depopulated as soon as possible. Furthermore, the model of Laevens et al. cannot be used if all pigs in a pen are seropositive, if one cannot point out the single pen with the highest seroprevalence in a compartment, or both. In contrast to weaned piglets and finishing pigs, breeding pigs in the Netherlands are individually housed in boxes or tethered. As a result, they have only direct contact with two neighbours Ð whereas weaned piglets and finishers usually have direct contact with nine or more pen mates. Reduction of the number of different individuals that have contact with each other can reduce the transmission between individuals (Koopman and Longini, 1994). Thus, transmission between breeding pigs may be lower than between weaned piglets and finishing pigs housed in groups. In this study, we quantified the transmission of CSF virus between breeding pigs in herds infected during the 1997±1998 epizootic in the Netherlands. To further examine the validity of the transmission parameter established, we used it to design a model to estimate the period in which the virus most-probably entered the herd. Subsequently, we tested this model using the serological results of 34 breeding sub-herds. We were unable to estimate transmission parameters for weaned piglets and finishing pigs from data collected during the epidemic. This is because only a sample of these pigs had been tested. However, by use of the experimental results of Laevens et al. (1998a), (1999), and Bouma et al. (1999), we designed a model thats describes the transmission of CSF virus within compartments with several pens housing finishing pigs. To test this model Ð and thus test whether the transmission during the epidemic did not differ from the transmission observed during the experiments Ð we used it to estimate the period of virus introduction in 41 finishing and weaning sub-herds. In contrast to the model of Laevens et al. (1998b), this back-calculation model describes the transmission within and between pens and requires only a limited sample size. 2. Materials and methods 2.1. Herds The study included 82 of the 429 herds that were diagnosed as CSF virus-infected during the 1997±1998 epidemic in the Netherlands. Of these 82 herds, only a single

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contact with a herd infected earlier on during the epidemic had been detected. Furthermore (on the basis of their disease history and serological findings), within the 1km radius around these herds Ð they were the first herds to be infected by the virus. We assumed that in each of these 82 herds, the virus had been introduced by the single contact that was known. This contact could be either  animals from an infected herd (animal),  a pig transportation lorry that visited an infected herd earlier on the same day (lorry),  a person (in contact with the pigs) who visited an infected herd earlier on the same day, or mutual use of equipment (visitor),  storage of manure from an infected herd or use of common equipment to distribute manure (manure), or  semen from an infected boar centre (semen). Each of these types of contacts is considered a sufficient cause for the introduction of CSF virus into a herd (Terpstra, 1987; De Smit et al., 1999). From the clinical history (which pigs showed the first clinical signs) and serological findings (which pigs were seropositive) it was decided in which part of the herd the virus had been introduced. In 41 of the herds, the chain of infections started in the population of breeding pigs; in the other 41 herds, the infection started among the weaned piglets or finishing pigs. Some characteristics of the 82 herds are listed in Tables 1, 2 and 3. 2.2. Sample collection and serological tests Before infected herds were depopulated, blood samples had been collected from pigs in all parts of the herd. The number of samples that were collected in the part of the herd (population of breeding stock, or a compartment housing finishing pigs or weaned piglets aged 8 weeks or more) where the infection had started, is listed in Tables 1, 2 and 3 for the herds included in this study. Serum derived from each of the blood samples was tested for antibodies against CSF virus in the Ceditest1 ELISA (Colijn et al., 1997). To make the serological testing CSF specific, samples that twice showed an inhibition 30% were retested in the neutralising peroxidase-linked assay (NPLA) as described by Terpstra Table 1 Characteristics of seven herds with a single contact with a herd that was infected earlier during the epidemic and where the infection of CSF virus started among the breeding pigs Herd

Type of contact

Number of days observeda

Number of breeding pigs

Number of finishers

Breeding pigs seropositive

r (dayÿ1)

1 2 3 4 5 6 7

Semen Animal Lorry Visitor Lorry Lorry Visitor

47 42 49 56 57 45 57

130 173 181 170 148 127 399

868 1007 37 581 83 0 1879

17 11 14 69 36 35 85

0.10 0.10 0.087 0.11 0.093 0.13 0.12

a Number of days observed: number of days between contact and sample collection; r: epidemic growth-rate parameter.

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Table 2 Characteristics of 34 herds with a single contact with a herd that was infected earlier during the epidemic and where the infection of CSF virus started among the breeding pigs Herd

Type of contact

Observed Upper Lower Number of daysa estimate estimate breeders

Number of Breeders Breeders Probability finishers tested positive

8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41

Lorry Animal Lorry Semen Semen Semen Visitor Visitor Semen Semen Semen Visitor Visitor Visitor Manure Semen Lorry Lorry Lorry Visitor Visitor Visitor Visitor Lorry Visitor Visitor Visitor Visitor Manure Lorry Lorry Visitor Visitor Lorry

37 24 24 26 22 43 10 29 42 38 38 22 48 48 24 55 16 18 28 48 33 21 29 44 35 29 50 42 27 10 42 37 41 34

66 0 717 0 125 120 641 156 289 567 1752 648 156 661 398 519 17 128 967 0 706 343 277 1137 187 0 0 625 3845 287 1225 938 162 611

50 44 49 51 44 66 40 53 70 61 62 47 48 55 44 58 47 48 45 79 49 50 41 59 63 45 65 47 54 43 46 46 53 59

24 10 10 21 18 35 11 26 38 10 33 17 23 26 9 29 9 17 11 42 10 9 9 32 35 16 36 23 23 9 27 21 29 33

227 249 606 214 155 270 116 143 158 103 227 103 88 188 152 194 207 298 211 265 451 512 145 137 124 370 247 109 441 218 583 323 170 196

50 63 86 48 41 43 38 40 38 14 57 21 30 48 40 51 40 54 55 46 75 76 42 43 36 82 51 37 90 62 77 175 67 73

2 0 0 2 1 5 0 2 8 1 6 1 3 3 0 4 0 1 0 10 0 0 0 5 6 1 7 2 2 0 4 8 4 5

0.70 0.99 0.80 0.46 0.43 0.73 0.13 0.36 0.39 0.74 0.48 0.46 0.07 0.20 0.98 0.09 0.46 0.21 0.87 0.50 0.67 0.69 0.67 0.84 0.20 0.96 0.73 0.17 0.37 0.18 1.00 0.26 0.70 0.19

a Observed days: number of days between contact and sample collection; Upper estimate: upper limit of the 95% CI estimated by the model; Lower estimate: lower limit of the 95% CI estimated by the model; Probability: the probability under the model of the observed outcome or a more extreme one. The combined 2 goodness-offit statistic was 58.6 (d.f. 68), resulting in a combined probability of 0.784.

et al. (1984), using CSF strain Brescia and border disease virus (BDV) strain F and bovine virus diarrhoea virus (BVDV) strain Oregon. Because we want to describe within-herd transmission from the serological results of a herd, the probability of a positive serological test result as a function of the time elapsed since infection of an individual pig has to be included in the analysis. On the basis of their difference in test mechanism (biochemical assay (ELISA) versus bioassay (NPLA)), we

Type of contact

Observed daysa

Upper estimate

Lower estimate

Number of sows

Number of finishers

Finishers tested

Number of pens

Pigs positive

Probability

42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70

Animal Animal Animal Lorry Animal Animal Lorry Visitor Animal Animal Lorry Lorry Manure Visitor Lorry Visitor Animal Visitor Visitor Lorry Lorry Lorry Visitor lorry Visitor Lorry Lorry Lorry Visitor

29 12 14 16 22 23 38 29 14 21 20 25 20 30 27 38 14 39 42 42 34 41 30 51 29 16 13 25 30

49 29 29 27 27 29 45 49 31 33 32 33 45 41 40 49 29 52 46 49 42 48 33 52 31 44 31 39 29

34 9 9 9 9 9 32 9 9 9 9 9 9 26 19 33 9 34 30 36 9 37 27 36 9 9 9 9 9

0 0 0 142 0 0 0 0 0 0 264 149 0 0 0 22 0 0 479 121 0 0 0 991 0 0 0 415 183

2624 3905 789 805 594 447 1497 1029 739 191 1189 1121 282 88 126 344 633 422 1091 1028 467 711 19 1394 350 256 578 756 1644

12 10 10 10 8 12 12 12 6 8 10 6 6 12 6 7 10 8 6 9 8 24 1 12 21 4 8 10 8

24 10 10 20 16 24 24 3 11 8 10 6 3 12 6 10 20 5 6 9 5 24 19 12 21 2 9 7 24

9 0 0 0 0 0 11 0 0 0 0 0 0 3 1 5 0 3 2 5 0 15 10 7 0 0 0 0 0

0.01 0.40 0.58 0.90 0.49 0.59 0.83 0.98 0.65 0.81 0.89 0.45 0.65 0.47 0.41 0.03 0.66 0.43 0.31 0.85 0.42 0.50 1.00 0.10 0.07 0.45 0.50 0.92 0.02

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Herd

206

Table 3 Characteristics of 41 herds with a single contact with a herd that was infected earlier during the epidemic and where the infection of CSF virus started among the finishing pigs or weaned piglets

Lorry Lorry Visitor Lorry Visitor Visitor Visitor Lorry Manure Animal Visitor Visitor

20 33 18 52 20 30 18 36 47 26 33 49

35 48 31 60 38 31 30 44 60 28 38 59

9 34 9 35 9 9 9 31 50 22 19 47

221 293 203 0 0 199 0 0 0 0 272 0

878 714 1100 321 551 1387 247 585 790 506 868 181

8 10 10 10 8 10 15 8 10 10 7 10

7 20 10 6 6 10 15 8 10 80 8 10

0 10 0 3 0 0 0 2 6 3 1 10

0.86 0.05 0.96 0.75 0.80 0.07 0.98 0.74 0.01 0.80 0.58 0.08

a Observed days: number of days between contact and sampling; Upper estimate: upper limit of the probability distribution estimated by the model; Upper estimate: upper limit of the number of days between contact and sample collection estimated by the model; Lower estimate: lower limit of the number of days between contact and sample collection estimated by the model; Probability: the probability under the model of the observed outcome or a more extreme one. The combined 2 goodness-offit statistic was 87.1 (d.f. 82). This resulted in a combined probability of 0.329.

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71 72 73 74 75 76 77 78 79 80 81 82

207

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assumed that the test result of the Ceditest1 ELISA was independent from the test result of the NPLA. The probability that a CSF virus-infected pig is positive in the test combination described above (Probc) is then Probc ˆ ProbELISA ProbNPLA

(1)

with ProbELISA the probability that a CSF virus-infected pig is positive in the ELISA, and ProbNPLA the probability that a CSF virus-infected pig is positive in the NPLA. We derived a function of the dynamics of the combined probability of observing a positive test result in an individual pig as a function of the number of days since infection (t, t ˆ 0 at infection). To that end, we used data from experiments in which pigs were tested two times a week upon inoculation of the virus (Colijn et al., 1997; Bouma, unpublished observations). It showed that the function Probc …t† ˆ

0:99374 1 ‡ eÿ0:4806…tÿ18:4512†

(2)

is a good description of the probability of observing a positive result in the combination of the two serological tests used as described above, because it explains 99.8% of the experimental observations. A graphic reproduction of this function is shown in Fig. 1. 2.3. Analysis of data 2.3.1. Transmission of CSF virus between breeding pigs We assumed that transmission in a herd can be described by the stochastic SIR model (see e.g. de Jong (1995)). In this random-mixing model, S is the number of susceptible animals, I the number of infectious animals and R is the number of recovered animals (which are considered immune). Infection of susceptible pigs occurs with rate SI/N and recovery of infectious pigs occurs with rate I, with and  the infection-rate parameter and recovery-rate parameter, respectively. In the beginning of the infection (when the number of infectious and resistant breeding pigs is limited compared to the number of susceptible ones), the number of infected animals as a function of the time since introduction of the virus, I(t), can be described as I…t† ˆ I0 ert

(3)

with t the number of days since introduction of the virus; I0 the number of infectious breeding pigs at t ˆ 0; and r the growth-rate parameter. We estimated r from the serological results of the 7 herds listed in Table 1. In these herds, all breeding pigs were tested for antibodies to CSF virus. The growth-rate parameter was estimated with a generalised linear model (GLM), with a logarithmic link function and a Poisson error term (McCullagh and Nelder, 1989). In this GLM, the number of days between contact and sampling minus the average number of days between infection and seroconversion was fitted with the fraction of seropositive sows as the response variate. From formula (2), the average number of days between infection and seroconversion was estimated at 18.45 days. Because we assumed that the infection started with one infectious individual, the logarithm of the inverse of the total number of

A. Stegeman et al. / Preventive Veterinary Medicine 42 (1999) 201±218 Fig. 1. Regression curve of the probability of a positive result in the combined serological tests used in this study with time since experimental inoculation of CSF virus.

209

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breeding pigs was included as offset variable in the model. To check the fit of the model, we calculated Pearson's 2 goodness-of-fit statistic and plotted the standardised residuals against the fitted values. Furthermore, we validated the growth-rate parameter established by the GLM by use of the results of herds 8±41 in Table 2. In these herds, only a sample of the breeding pigs had been tested. The sampling protocol prescribed sampling every nth pig. (n was not constant throughout the epidemic, but can be derived from the ratio between the number of pigs present and the number of pigs tested in Table 2.) For each of these 34 herds, the lower and upper limits of the 95% confidence interval (CI) of the seroprevalence was estimated by (Cochran, 1977): s Nÿn (4) L ˆ p1:96 p…1ÿp† …Nÿ1†n in which p is the observed seroprevalence in the breeding stock, N the number of breeding pigs present and n is the number of breeding pigs tested. If the observed seroprevalence was 0, the upper limit of the CI was estimated by (Cannon and Roe, 1982):  n (5) L ˆ …1ÿ…1ÿ0:95†1=n † Nÿ ‡ 1: 2 Assuming I0 ˆ 1, from (3) it follows that tˆ

ln…npos † ‡ 18:5 r

(6)

with t the number of days since introduction of the virus and npos the number of seropositive breeding pigs. For each of the 34 herds, in Eq. (6) we varied npos from the lower to the upper limit of the estimated CI of the seroprevalence and r from the lower to the upper limit of the CI estimated for the seven herds in Table 1. Subsequently, all outcomes of t were combined to estimate Ð for every single day before the herd was tested Ð the probability that virus was introduced into the herd. In these calculations, we assumed that r was normally distributed around the value that resulted from the GLM. In this way, a probability distribution for the number of days between virus introduction and sample collection was calculated for each herd. Because we assumed that the infection started with one infectious animal (see above) and these herds were diagnosed after observing suspicious clinical symptoms, we assumed that a herd could not be detected before animals in the second generation (infected by the animal that started the disease) were clinically ill. This implies that the minimal period between virus introduction and diagnosis herds where no seropositive breeding pigs had been observed was set at 9 days. From the probability distributions we estimated, for each herd, the expected number of days between introduction of the virus and sampling as X (7) E…t† ˆ pt t with pt the probability that a herd became infected on day t before sampling. Next, we calculated for each herd the probability under the null hypothesis (r of the 34 herds ˆ r in

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the model), of observing this outcome or a more-extreme one (two-sided). All these test probabilities (p) were combined as X ÿ2 ln…p†; (8) which follows a chi-square distribution with 2n degrees of freedom (after an idea by Fisher; see e.g. Sokal and Rohlf (1981)). The model was rejected if the P-value of this chi-square statistic was less than 0.05. If the model was not rejected, we estimated R0 for the breeding pigs. For the estimation, we used the approach described by Pielou (1977). Shortly, if I(t) is the number of infected animals at time t (Eq. (3)), then the number of infected animals 1 generation further (time t ‡ T) is equal to I…t ‡ T† ˆ R0 N…t†

(9)

described in discrete intervals of T, and I…t ‡ T† ˆ N…t†erT

(10)

described in continuous time. Combination of Eqs. (9) and (10) results in R0 ˆ erT

(11)

with T the mean generation interval (average time between infection of an individual and infection of the individuals that are infected by this individual). From Laevens et al. (1999), we estimated that T equals 10 days (range 9.0±12.1). 2.3.2. Transmission of CSF virus between finishers and weaned piglets A simple model was designed based on the observations in transmission experiments of Laevens et al. in 12 to 15-kg weaned piglets (1998a) and very heavy (>120 kg) slaughter pigs (1999) (supported by observations of Bouma et al. (1999) in 12-week-old pigs). Their results show at what time pigs in the same or an adjacent pen become infected when exposed to CSF by one pig inoculated with CSF virus. As with the breeding pigs, we assumed that the infection started with one individual. Consequently, Eq. (2) describes the probability that the pig first infected is seropositive at time t after introduction of the virus. In the model, the other pigs in the pen where the infection started were infected between days 4 and 19 upon introduction of the virus according to a uniform probability distribution. The probability that the pen-mates of this pig are seropositive at time t is equal to the probability that these pigs already have become infected (see above) multiplied by the probability that they have seroconverted (Eq. (2), relative to the time of infection of the individual pig). If we randomly sample a pig in this pen at time t, it may be the pig that started the infection (1/total number of pigs in the pen (tnp)) or one of his pen mates ((tnpÿ1)/tnp). Combination of the above-shown dynamics of infection, dynamics of seroconversion and sample collection results in the probability that a seropositive pig is sampled in the pen where the infection started at t days after introduction of the virus (pft). The pigs in the other pens in the compartment were infected between days 10 and 29 upon virus introduction (also according to a uniform probability distribution). On the same way as described above for the pen first infected, the dynamics of infection, the dynamics of seroconversion and sample collection were

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combined to obtain the probability that a seropositive pig is sampled in each of the secondary infected pens at t days after (pst). For each herd in Table 3, the compartment where the disease started was selected on the basis of the clinical history and serological findings. If one sample per pen is tested and one or more samples are positive, for each day the probability of the observed outcome can be described as     mÿ1 xÿ1 mÿ1 x mÿx pst …1ÿpst † ‡ …1ÿpft † pst …1ÿpst †mÿ1ÿx (12) Prob ˆ pft xÿ1 x and if all samples are negative this probability is Prob ˆ …1ÿpft †…1ÿpst †mÿ1

(13)

with m the number of pens; x the number of positive samples; pft the probability that a seropositive pig is sampled in the pen where the infection started at t days after introduction of the virus; and pst is the probability that a seropositive pig is sampled in the other pens in the compartment at t days after introduction of the virus. If more or less than one pig per pen was tested, Eq. (12) and (13) were adapted accordingly. This procedure results in a distribution per herd of the probability that the herd was infected for every single one of the days before the sample collection. As with the breeding pigs, if a single seropositive pig had been found, the minimal period between virus introduction and diagnosis in the herds was set at 9 days. From the probability distribution, we estimated the number of days between introduction of the virus and sampling according to the model by Eq. (7). Subsequently, we calculated for each herd the probability (two-sided), under the null hypothesis (transmission proceeds as predicted by the model), of observing this outcome or one that was more extreme. All probabilities (p) were combined as described by Eq. (8) and the model was rejected if the P-value that accompanies the resulting 2 statistic was 0.05. 3. Results 3.1. Transmission of CSF virus between breeding pigs The serological data of the seven herds in which the entire breeding population was tested for antibodies against CSF virus is listed in Table 1. The corresponding value of r in these herds is also shown in this table. From the serological results, the average value of r was estimated at 0.108/day (95% CI: 0.060±0.156). Residual analysis showed that Pearson's 2 goodness-of-fit statistic was 0.39 (d.f. ˆ 6, p ˆ 0.99). The plot of standardised residuals against fitted values revealed no evidence of a pattern in variance and standardised residuals were between 0.4 and ±0.4. In Table 2, the observed seroprevalence is listed of the 34 herds where only a part of the breeding stock had been tested for antibodies against CSF virus. The estimated period of virus introduction (relative to the date of sample collection) is also shown in this table. In addition, the relation between the number of days between the estimated day of virus

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Fig. 2. Number of days between virus introduction and sample collection estimated by the model plotted against the observed number of days between contact and sampling in 34 herds where the infection started in the population of breeding pigs.

introduction and sampling and the number of days between the registered day of contact with a previously infected herd and the day of sample collection is plotted in Fig. 2. The supposed starting date for all 34 herds was within the 95% confidence period estimated by the model. For each of these herds, the probability under the model, of the observed outcome or a more-extreme one is shown in Table 1. The combined 2 goodness-of-fit statistic was 58.6 (d.f. 68), resulting in a combined probability of 0.784. Thus, the hypothesis that the model with the previously estimated transmission parameter could describe the CSF virus transmission in these herds, was not rejected. Subsequently, R0 was estimated as 2.9. 3.2. Transmission of CSF virus between finishing pigs and weaned piglets The serological results of the 41 herds where the infection started in the weaner or finisher section are shown in Table 3. The estimated period of virus introduction (relative to the date of sample collection) is also shown in this table. The observations of 36 of the 41 herds fitted within the 95% confidence period. In Fig. 3, a plot is shown of the observed number of days between contact and sampling on the X-axis and the number of days estimated by the model on the Y-axis, including the observations of all 41 herds. For each herd, the probability under the model, of the observed outcome or a more extreme one is shown in Table 3. The combined 2 goodness-of-fit statistic was 87.1 (d.f. 82). This resulted in a combined probability of 0.329. Consequently, the hypothesis that the transmission of CSF virus in these 41 herds was similar to the transmission observed under experimental conditions was not rejected. 4. Discussion In this study, we quantified and modelled the transmission of CSF virus among breeding pigs in herds infected during the 1997±1998 epizootic in the Netherlands.

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Fig. 3. Number of days between virus introduction and sample collection estimated by the model plotted against the observed number of days between contact and sampling in 41 herds where infection started among the finishing pigs or weaned piglets of 8 weeks or older.

Furthermore, we extrapolated the results of experimental transmission studies of Laevens et al. (1998a), (1998b) and Bouma et al. (1999) to model the transmission of CSF virus within compartments housing finishing pigs or weaned piglets of 8 weeks or older. The models of the transmission in populations of breeding stock as well as in finishing pigs and weaned piglets were tested with the serological results observed in herds from which only one upward contact had been traced. In populations of breeding pigs, r was estimated as 0.11 per day and R0 as 2.9. Thus, transmission of CSF virus seems lower among sows than among weaned piglets and slaughter pigs (Laevens et al., 1998a, 1999). Because the housing system of the breeding pigs restricts the number of different animals that can have direct contact with each other Ð as compared to the housing systems of weaned piglets and finishing pigs Ð this finding was not unexpected. Furthermore, one could speculate whether age resistance is partly responsible for the difference. It is remarkable that, although the assumption of random contacts of the SIR model is violated by the more or less individual housing system of the breeding pigs, the fit of the model is good. This may be caused by actions of the pig keeper, such as moving individual sows from one box to another, move up groups of sows from one room to another on the basis of their phase in the reproductive cycle, injecting several sows with the same needle, and movement of the boar(s). The results of a study of Watts and Strogatz (1998) suggest that only a limited number of such actions are necessary to approximate a random contact structure. Furthermore, the results of Laevens et al. (1999) suggest that the virus may be transmitted by air within a farm, in which case the pigs can have contact with a large number of other pigs. Finally, the SIR model appeared also to be a good model to estimate the transmission of pseudorabies virus among breeding stock under the same housing conditions (Van Nes et al., 1996). The combination of the relatively low R0 and the estimated generation time of 10 days indicates that CSF virus will spread rather slowly in populations of breeding pigs as

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compared to weaned piglets and slaughter pigs. From Eq. (3) it follows that the time to double the number of infected pigs is 6.4 days among individually housed breeding pigs (r ˆ 0.11 per day), whereas it is only 1.6 days among weaned piglets (r ˆ ln(R0)/ T ˆ ln(81)/10 ˆ 0.44) and 2.6 days among finishing pigs (r ˆ ln(R0)/T ˆ ln(14)/ 10 ˆ 0.26). If we also take the age resistance to clinical disease into account (Van Oirschot, 1992), this implies that the virus may be present in populations of breeding stock for quite some time before it is noticed and also that an infected herd will be detected sooner if the infection starts in the weaner or finisher section than when the infection starts among the breeding stock. The latter is supported in this study by the comparison of the number of days between contact and sample collection in herds where the infection started in the breeding population and the herds where it started in the weaner or finishing section. The average number of days is significantly (p ˆ 0.008 in the Mann-Whitney U-test) higher in the first group (36 days, sd ˆ 13) than in the latter (28 days, sd ˆ 11). Consequently, quite often the virus may have been transmitted to another part of the herd before CSF is diagnosed. If the virus transmits at a higher level in these secondary infected groups of pigs and if these pigs are more susceptible to clinical disease, the diagnosis CSF can be based on the examination of pigs other than breeding pigs. This stresses the necessity to serologically examine all parts of an infected herd in order to find out where the virus was introduced. Such knowledge is important to find out by which contact the virus entered the herd. Another implication of the relatively low breeding pig, R0, is the considerable chance that the virus will fade out by chance after having infected only one or a few animals (minor outbreak). Theoretically, the chance of a minor outbreak is Rÿ1 0 ˆ 0.34 (Metz, 1978). If a minor outbreak includes sows in the critical part of gestation, it may give rise to carrier sows. Such sows give birth to persistently viremic piglets that start spreading the virus anew (Terpstra, 1987). The fraction of herds with a minor outbreak is probably less than predicted above, because virus may often be introduced into a herd more than once, the infection may start with more than one animal, or transmission of the virus from sows to piglets or finishing pigs may cause a major outbreak in another part of the herd. However, to minimise the risk of new virus transmission by the piglets of carrier sows later on, it is advisable to trace minor outbreaks in sow populations that have been at risk for virus introduction, before declaring regions free of CSF virus. As with any study, this one also has its limitations. First of all, the results are based on the contacts that had been traced by the veterinary authorities. We cannot exclude that contacts may have been missed during this tracing (e.g. because the farmer did not report all contacts). Secondly, because the model assumes exponential growth, it cannot be used to estimate the period in which the virus entered in herds with a high seroprevalence (maximum seroprevalence in this study was 40%). In addition, the estimate of R0 is very sensitive to the value of T used, and the latter parameter was not derived from the same set of data. Furthermore, if introduction of the virus results in a minor outbreak, the model cannot be used and naturally it can also not be used if the infection starts with a carrier sow and transmission of the virus within the herd does not start until the persistently viremic piglets are born. Finally, a high seroprevalence against other pestiviruses such as BVDV or BDV most likely influences the transmission of CSF virus and thus hampers the use of the model.

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In the second part of this study, results of experimental transmission of CSF virus were extrapolated to describe transmission of CSF virus in compartments of pigs. The fit of the model was satisfactory. Thus, it is concluded that the transmission between weaned piglets and finishing pigs during the 1997±1998 epidemic in the Netherlands was not significantly different from the transmission observed under experimental conditions. However, Fig. 3 shows that the estimated time since introduction of the virus seems to relatively increase a little as the time between contact and sampling increases. This may have been caused by the fact that the physical separations between the pens (which consisted of a solid wall in the experiments) might have been only bars in some of the herds included in this study. Another possibility is that the infection may have started in more than one animal, in more than one pen, or both. Furthermore, the pig keeper may have enhanced transmission. If pigs become clinically ill, a pig keeper will usually treat his animals by injection and may transfer the disease in the process. This may also occur in the process of removing dead pigs out of a compartment. However, the fit of the model became better if the time that the affected animals stayed in the herd is included (a herd can never be infected before the animals in which the disease started entered the herd) (2 ˆ 77.0, d.f. ˆ 82, p ˆ 0.64 in the present study). Laevens et al. (1998b), described a model to estimate the period of virus introduction in weaned piglets. However, their analysis was restricted to the pen level. This implies that if not all pigs in a pen are tested, or all pigs in a pen have antibodies to CSF virus, or both, their model cannot be used. The model presented here does not have that limitation. Only if all pigs in a compartment have antibodies to CSF virus, can our model not be used. However, during the epidemic described in this issue (Elbers et al., 1999) there were very few observations of a compartment in which only seropositive pigs had been sampled and no signs of active virus circulation were observed. To estimate the period in which virus was introduced into these herds, a model describing the transmission of CSF virus between compartments has to be designed. Adaptation of the model is also necessary, if pigs are transferred from one compartment to another. In that case, the movements of the pigs over time have to be included in the model Ð otherwise, the period between sampling and virus introduction will be underestimated (seropositive pigs will be dispersed over several compartments of the herd, suggesting that the infection started in several compartments at approximately the same time). Finally, we do not know whether the between-pen transmission as derived from the experiments is applicable to very large compartments or in pig houses without compartmentalisation. It may be possible that the period in which the pigs in the other pens become infected will expand over a longer period than the 10±29 days used in this study. However, after inoculation of CSF virus in one pig in one room, Laevens et al. (1999) did not observe a significant difference between the time that pigs in the adjacent pens in the same compartment became infected as compared to the time that pigs in a pen of an adjacent compartment became infected. This observation suggests that the period necessary for between-pen transmission of CSF virus probably will not increase sharply as the number of pens in a room increases. A drawback of our model is its deterministic nature. However, because the study only includes major outbreaks, we did not have to take into account that the infection may fade out by chance shortly after introduction. On the other hand, stochastic processes in the

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initial phase of infection (when infection goes from 1 to approximately 5 infected individuals) may cause the infection to proceed more or less quickly than predicted by the model at that time. However, because R0 is high among weaned piglets and slaughter pigs, the influence of this stochastic effect is probably limited to a few days (in a pen of 10 pigs, this additional variation is approximately 30% of the generation interval of 10 days as estimated by Velthuis and de Jong (unpublished)). The results of this study can be used in several ways. First of all, the models described can be used during epidemics to estimate the period in which the virus most likely entered an infected herd. Such information is of great use to the veterinary authorities, because they can focus their upward and downward tracing of infected herds to specific time periods. Especially in an area with a high pig density this is important, because of the limited manpower and the huge number of herds to be visited. To make the estimated period in which the virus most likely entered a herd as short as possible, we advise testing a large number of pigs in infected herds (including all sows). While using the models described here one should, however, realise that other CSF-virus strains may have spreading capacities different from the one that caused the 1997±1998 epidemic in the Netherlands. Therefore, it is advisable to test during an epidemic from the results of herds with a known moment of infection whether these models fit to the observations. If necessary the models can be adapted accordingly. The model should also be adapted if the characteristics of the serological testing are different. Secondly, our results can help to analyse the effectiveness of intervention measures that have been implemented during an epidemic (Stegeman et al., 1999). Thirdly, knowledge of within-herd transmission is necessary in modelling studies that estimate the effectiveness of intervention measures or design effective monitoring programmes. 5. Conclusions In this study, we quantified and modelled the transmission of CSF virus among breeding pigs in herds infected during the 1997±1998 epizootic in the Netherlands. In populations of breeding pigs, r was estimated as 0.11 (0.060±0.156) per day and R0 as 2.9. Furthermore, the transmission observed in compartments housing weaned piglets and finishing pigs was in agreement with experimental observations described by Laevens et al. (1998a), (1999).

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