Appendix 13

Appendix 13

Modelling Foot-and-Mouth disease: A comparison of epidemiological models

François MOUTOU, Benoît DURAND AFSSA, LERPAZ, Epidemiology Unit, BP 67, 94703 Maisons-Alfort cedex, France Tel : 33 1 49 77 13 33, fax : 33 1 43 68 97 62, E mail : f.moutou@alfort.afssa.fr

Introduction

Models have been used for some times with the aim of helping in decision making around Foot-and-Mouth Disease (FMD) outbreaks. However, up to very recently, most of these models could mainly be seen as training tools, because Western European and North American countries, as well as Australia and New Zealand, where many of them have been developed, had been free of FMD for many years, or even never experienced the disease like New Zealand. In fact, most of the data used were those collected during the 1967-1968 UK epizootics, under farming conditions certainly different from those prevailing today. More recently, with the sanitary measures –ban on vaccination– implemented over Europe, a new demand arose. However, most of the models were still used either as tools to better understand FMD virus transmission including airborne transmission, to mimic an outbreak, for training purposes, or to compare economical scenarios. The 2001 epizootics, bringing a lot of new data about FMD transmission under today farming conditions, was the occasion for new modelling. In the UK, during 2001, different models were run and published, with conclusions used to control the disease by the authorities. Here we try to present and to compare these models, from what has been published.

What is modelling?

Modelling is by no means a new tool in epidemiology, even if the development of smaller but much more powerful and easier to use computers -and software- certainly helped a lot. If modelling is aimed at a better understanding of reality and is seen as an instrument in decision making, it more often pinpoints where data are lacking or where understanding of a natural phenomenon is still to be improved. Modelling in epidemiology cannot be seen without a strong connection with field data, even if it should be able to bring help to take decision when not everything is known, a classical situation. FMD is a good example of a disease that can be computed, at least in our west European farming conditions, due to: -fast spreading of the virus through airborne route to four domestic species, -officially good agricultural statistics, -knowledge of animal movements, -the absence, up to now, of wild reservoirs or vectors.

During the spring of 2001, different teams made projections, from the beginning of the epizootics, to predict its probable size and duration. A recent synthesis already compared these results (Kao 2002). The present paper will use this reference at large.

Modelling FMD in the UK in 2001

Beside the surprise that such an epizootic may represent, it is worth giving of it a good description. In fact, it is only at the end of the year 2001 that such publications were accessible (Gibbens et al. 2001) even if data where already present at the DEFRA. Of course, at the end of February 2001, very few was known. The different teams involved used different approaches, more linked to their own previous modelling experience than to FMD knowledge. The main model categories include deterministic differential equations, micro-simulation, spatial models, and the models could be deterministic or stochastic. In every case, parameters had to be estimated and this proved to be difficult. One of the most classical index is the so called Current Case Reproductive Rate (CRR), which is a transmission parameter indicating how many new outbreaks an existing infected premise (IP) will create. If the value is over 1, the epidemic will increase, if it is below 1, it is decreasing and probably under control. Most of the models are testing their own parameters against this threshold value.

Spatial structure of the countryside was of importance, as the distance between farms and between sensitive animals was one of the key to the problem (Morris et al. 2001). However, distance is a difficult parameter to address as it can be seen as a geographical dimension but also as a functional relationship (dairy farms are closer to each other than dairy and beef farms over the same area, as different people, traders, technicians, veterinarians, will visit them). “Moment-closure”, i.e. the density of farms clusters, or “contact matrix”, i.e. distances between pairs of farms, were two sophisticated ways to give value, under many hypotheses, to such distances. The “moment closure” was used by Ferguson et al. (2001). It relies on clusters of farms and on density of farms clusters. The model estimates the probability of virus transmission between farms and farm clusters. The “contact matrix” was used by Keeling et al. (2001): it integrates the distance between farms when estimating the probability of virus spreading should one farm becomes an IP. Each farm could also vary in susceptibility through parameters like: distance to an IP, to a pig farm, to a slaughterhouse, to a road, or to a large farm, and like known commercial links with an IP. One of the main questions asked early during the epidemics, was the culling strategies (and/or the vaccination strategies) to implement, how (delay between suspicion/diagnosis and culling for instance) and why. Such different kind of premises as the following were considered: infected premises (IP), direct contact premises (DC), contiguous premises (CP), premises within 3 km of an IP. The discussion was mainly around a comparison of the results of shorter delays versus longer delays to cull IP animals and/or DC and CP animals. Not only epidemiological considerations were seen, but also economical points of view. This may explain why the no vaccination scheme was preferred.

Results

Beside the “official” publications, it was also possible to use other information source, through internet, and the following figure is one example (figure 1). It is all working with a logistic model. Other information than just epidemiological or even economical data are added! Such figure, and others, could be found at: http://www1.tpgi.com.au/users/kpduffy/fmd.htm The global shape of the epidemic is clearly seen on this figure. It also compares it with the 1967-1968 epidemic. If the model’s fit is rather good for the beginning of the epidemic, the predicted tail is much shorter, but comparison and interpretation must be cautious.

This figure (and this model) is mainly descriptive but recalls when different important decisions were taken.

Figure 1. A simple descriptive model based upon the logistic equation.

The comparison of culling scenarios came with the other modelling approaches.

Figure 2. Comparison of the predicted epidemic curves under various control strategies with a deterministic model (Ferguson et al., 2001a)

In the case of Ferguson and co-workers (2001a, 2001b), the question is really to look for the control of the epidemic though shorter delays between diagnosis (or clinical suspicion) and culling, i.e. the end of virus excretion by animals (figure 2). Only scenarios with culling of IP and of farms in the surroundings, within a short period of time, will lead to a CRR below 1, i.e. a control of the epidemic. It is however already well known that waiting too many days to cull infected animals will not be a good politic during an outbreak of FMD.

Figure 3. Comparison of the predicted epidemic curves under various control strategies with a stochastic model (Keeling et al., 2001)

Black: data (reported daily cases), Pink: 100 runs of the model, Red: mean daily value of the 100 runs

1.0 0.8 0.6 0.4 0.2 0.0

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

Epidemics duration (weeks)

SO SODC SOV2

1 0.8 0.6 0.4 0.2 0

0 40 80 120 160 200 240 280 320 360 400 440 480 520 560 600 640

Epidemics size (outbreaks)

SO SODC SOV2

Figure 4. Cumulative distribution of the predicted epidemics size and durations under three control strategies (Durand and Mahul, 2000)

SO: IP cull only, SODC: IP and dangerous contacts cull, SOV: IP cull and ring vaccination from the end of the 1st week

1

0.8

0.6 Direct costs (mFF)

0.4

0.2

0

0 100 200 300 400 500 600 700 800 900 1000 1100 1200 SO SODC SOV2

1

0.8

0.6 Total costs, net of the EU subsidies, borne by the French economy (x1000 mFF)

Figure 5. Cumulative distribution of the predicted epidemics costs under three control strategies (Durand and Mahul, 2000)

0.4

0.2

0 16.05 16.20 16.35 16.50 16.65 16.80 16.95 17.10 17.25 17.40 17.55 SO SODC

SO: IP cull only, SODC: IP and dangerous contacts cull, SOV: IP cull and ring vaccination from the end of the 1st week

In fact, all figures 2 and 3 are trying to say the same thing, with different approaches: culling without vaccination is the best scenario to apply. Figures 4 and 5, by comparison, which were published in 2000, are discussing the same item but do not exclude vaccination (Durand and Mahul, 2000; Mahul and Durand, 2000). Here SO means stamping out of IP, SODC: stamping out of IP and of dangerous contacts, and SOV: stamping out of IP and ring vaccination from the end of the first week of the epidemic. The delay of one week is explained by saying that you certainly know a little more after one week, and that it may not be a good strategy to decide and to implement vaccination as soon as the first outbreak is known. These figures compare in terms of epidemic duration and size (figure 4) and in term of cost (figure 5) what will bring each strategy. Figure 4 can be read as the probability (y-axis) that an epidemic duration or size, respectively, will be less than a given value (x-axis). The shortest and smallest epidemics are obtained with the stamping out of IP and of dangerous contact culling policy, when the longest and largest is linked to stamping out of just IP. In terms of costs (figure 5), respectively direct and total, the best scenario is also with the SODC policy, even if for direct costs, SO (stamping out of just IP) is not so different.

Discussion

To be able to run such models as those published in nearly real time means that a lot of data had already been collected in the field. As the teams were not always the same, between those in the field and those computing a good coordination was necessary. However, from what is known today, the beginning of the epidemics was quite earlier than the time of the discovery of the first case, moment at which time the size, the geographical dispersion of the virus, the actual number of outbreaks and the distribution of the disease,

were not known and underestimated. FMD in sheep was not so well known in Europe and the importance of sheep trade, over Europe, was difficult to compute. The situation proved to be quite unique, so these models may be especially devoted to mimic FMD in sheep under conditions closed to February and March 2001 in United Kingdom. In the same time, deciding the shortening of the delays between suspicions and culling is a classical knowledge in case of FMD in our countries. The comparison made by Kao (2002) is clearly a modeller analysis, more than an epidemiological approach. The published papers brought a lot in term of methodology for models, maybe more than just in term of FMD epidemiology.

Acknowledgements

We thank Kris De Clercq who suggested this contribution, Michelle Rémond who presented it at the meeting, and the Research Group for support.

References

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