Archive: 1999 Session  Appendix 2
1999 Session of the Research Group of the Standing Technical Committee of EuFMDEffect of animal density on FMD spread
G. GERBIER, AFSSA Alfort, BP 67, 94703 MaisonsAlfort cedex
FMD outbreaks occurred in Western Europe quite a long time ago. Knowledge and consequently strategies might now be irrelevant in case of FMD infection, as animal density has dramatically increased. Classical Swine Fever in the Netherlands proved that highly contagious disease spread faster in densely populated areas. It was then decided in AFSSA (former CNEVA) to study the impact of density on the propagation of FMD.
Epidemiologists intuitively agree that density can increase the risk of disease but this have to be more deeply explained. A starting point is to understand what mean "animal density". This parameter is defined as the number of animals per unit area. It might not be adequate as the classical epidemiological unit is the herd, neither the animal nor the area. Another argument not to use animal density is the clustering of animals in herd. When we use animal density we imply that animals are uniformly distributed in space. But the way animals are clustered in farms suggest that animals from the same farm have a more similar risk and behaviour than animals from different farms. The information in animal density can be split in to two parameters: herd size and distance. Then analyzing the effect of animal density is reduced to the effect of herd size, distance and their interaction.
We have collected information from previous outbreaks that can give some information about density effect. Data come from many sources such as researcher database, report and articles. Scales are various: national to local. This information is gathered in a Geographical Information System (MapInfo ÿ). Analyses were focused on two aspects: airborne FMD and spatial correlation. To assess airborne spread we used the mathematical model developed by Moutou et al. (1986). Spatial analysis was performed using Splus statistical package. Spatial patterns were searched at the local scale (10km). Every time it was possible we tried to find risk factors at the herd level.
Results
Effect of density: analysis of Taiwan 1997
Taiwan is very informative as it happened nowadays within an industrialized pig production. As accurate data are missing, this is just a descriptive study.
FMD spread over the entire main island in 47 days after the notification of the infection (Figure 1). It can be seen in Figure 2 that, compared to FMD in UK in 196768, the spread was much faster. Within this epizootic the number of outbreaks per province is statistically linked to the number of farms in the province (p<104, Rñ=95%). For density the correlation is smaller.
Effect of herd size
Airborne emission of virus
The quantity of virus released in the atmosphere is directly linked to the number of animals. Theoretically, we should calculate this by summing the excretion of each infected animal every time lag. But as we have only little information to quantify the spread of infection in a herd, the quantity of virus is approximated by the maximum of virus released per time unit multiplied by the total number of animals. Infected herds are supposed to excrete virus 24h before the first clinical symptoms. Assuming a constant wind, the surface under the plume is linearly linked to the number of animals (Figure 3). Increasing the mean herd size will then increase the size of the population at risk.
Reception of the virus
Concentrations of virus inhaled by pigs have been calculated for the French data of C¡tes d'Armor in 1981. This epizootic was chosen because pigs were mainly involved. The evolution of the quantity of virus inhaled by one pig is shown in Figure 4. The cumulative quantity of virus inhaled by one pig varied from 2 particles to 1755. It seems that big herds are infected with lower doses of virus. When noninfected herds could be located, they were situated between outbreaks, more precisely in low doses of virus inhalation. With low doses, experimental infection was proved to be uncertain. From these data we have build a theoretical framework. Then we can assume a logistic doseeffect curve, the individual probability of infection is written:
Logit(P(animal infected)) = Logit(p) = a + b * dose = ? (2)
It is possible to represent the results found above with a simple model:
P(infected herd)=1(1P(animalinfected))^{size} (1)
If we change the function logit by a more practical function called complementary log log (cloglog(p) = log(log(1p))), we found that (1) become:
cloglog(P(herd infected)) = log(N) + ? (3)
This equation means that the curve linking the herd probability of infection and the dose inhaled by the animals is simply obtained by adding the logarithm of the herd size (at the cloglog scale).

The size only modify the intercept of the curve

With this model a bigger herd is infected sooner and with a lower dose

There are many combinations of size and dose inhaled leading to the same risk
The last item signify that a big herd far from the index outbreak can have a higher probability of infection than a closer but smaller herd. This would explain why some noninfected herds are found between outbreaks whereas the airborne route seems plausible. Size would act as a factor facilitating the infection.
Then, if the average size in one area increases the risk increases at least in two ways: risk emission and risk of reception.
Effect of distance
Distance is naturally included in the calculation of the airborne spread. But in many cases the source of the infection is unknown. We have then studied distance in a more general way. Using a delay of one week, we considered that were either emitter or receiver. We used the data of Westmidlands 196768 provided by M. HughJones to count the number of infected herds during the week t (receiver herd) surrounding a herd infected during the week t1 (emitter herd).
Figure 5 shows the evolution of the average number of infected herds within a given distance x from a herd infected the week before. Obviously the pattern is changing with time. As the mean, the distribution of the number is not constant (Figure 6). Around the peak of the epizootic (week 6 in this area), more than 10 outbreaks were found clustered around a herd infected a week before. After week 7, herds with 0 or 1 value are becoming the majority.
The example of Taiwan is very informative because it shows that dissemination rates can be more than 3 times the rates observed in UK in 196768 which were the reference parameters used by many authors. For example, Dijkhuizen (1994) used these parameters plus or minus 30% to study the economic impact of FMD. The small explicative value of density can be explained by the inefficiency of this parameter to describe the situation in Taiwan. Because of the mountains, it is not clear if the total area or the area without mountains has to be used.
The results on the effect of size on the probability of infection in pigs are quite new. Herd size has been designated has a risk factor in FMD by HughJones (1972) but on cattle: 68.3% of the dairy herds with more than 80 cows vs. 6.8% of the herd with less than 10 cows were infected in Cheshire in 196768. It is all the more important because concentration of pig in some areas is the principal problem we are facing. However, it is only one aspect of the problem as size can have other effect. Size is sometimes used in modeling as a surrogate for contacts and for a lot of factors linked to herd management. Estimation of the number of contacts in pig, cattle and mixed farms have been conducted by Nielen (1996) but size was poorly linked to the number of contacts between herds (Rñ=0.02). This contact pattern can change in an infected situation. Then, such results can then be used to assess the risk of introduction but not directly the risk of spread.
Our results suggest that the total amount of virus inhaled by the herd should be used to evaluate the risk instead of individual amount. This would be a way to rank the herds according to airborne risk. An important question is the choice of a cutoff value. With a too small value, too many herds will be identified at risk. At this point, it has to be noticed that there is a need for standardization of the mathematical model used to calculate concentration of virus.
Spatial analysis is complicated by the absence of information on noninfected herds. Our results demonstrate that outbreaks are clustered. But the next step, the estimation of the probability of infection according to the distance, was not possible.
In spatial analysis two situations can lead to the formation of cluster. On one hand the population is homogeneously distributed in space and there is an infectious process which creates a spatial dependence between cases. On the other hand the population is heterogeneous, there is no spatial link between cases but cases appear clustered in one place because there are more individuals at this place. Assuming a uniform spatial distribution of herds like Sanson (1994) in Interspread will clearly biased the estimation. We had found (data not shown) that this hypothesis was surestimating by around 30% the number of herds in Worcestershire. Moreover the size might influence the spatial distribution of herds. For example, because of grazing, bigger cattle herds probably have more land, then the distance between one herd to another should depend on herd size.
All these results confirm that the conclusions found earlier have to be reconsidered. But, unless more data will be available, it is impossible to disentangle the effect of herd size and distance.
The highest spread of FMD may arise if transmission of infection between herd was as successful as transmission within a herd. It was perhaps what happened in Taiwan. The results of all these studies show that if distance between herds and size increase in parallels the risk will clearly increase. But fortunately, at the moment, as the size of the herd goes up the number of herd goes down. Then there is a negative interaction between the two phenomenons: one is decreasing the risk, one is increasing it. As long as the data on noninfected herds will not be available, it will be difficult to assess the validity of different strategies.
Nevertheless, new strategies must be investigated. Preemptive slaughter is one solution but the right perimeter has to be estimated. In CSF, a 1 km perimeter seems to be efficient but too many epizootics were necessary to confirm it and CSF is less contagious than FMD. Another strategy can be to prevent the proximity of big herds.
 Figure 1 : Spatial and temporal spread of FMD in Taiwan in 1997
 Figure 2 : Comparison of estimated dissemination rate in Taiwan in 1997 and in UnitedKingdom in196768
 Figure 3 Surface of the area under the plume according to the number of pigs excreting for different quantity of FMD virus inhaled
 Figure 4 : Quantity of virus inhaled by one pig in each secondary infected herd (C¡tes d'Armor 1981)
 Figure 5: Average number of receiver herds (infected during week t+1) within a distance x from a emitter herd (infected during week t)
(Numbers correspond to the week of infection of the emitter)  Figure 6: Distribution of the number of receiver herds within 2 km from a emitter herd.
 Figure 6