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Foot and Mouth Disease 2001

For three years I worked at the University of Cambridge as part of a team of scientists modelling foot and mouth disease (FMD) in the UK. We had two broad aims: 
            • refine the mathematical models of the UK 2001 FMD outbreak, and
            • develop a vaccination control strategy for future outbreaks.
The work was funded by the Wellcome Trust. The other scientists were Mike Tildesley and Matt Keeling (modellers) from the University of Warwick; Rob Deardon and Steve Brooks (Bayesian statisticians) from the University of Cambridge; Darren Shaw, Shaun Abeysinghe and Mark Woolhouse (epidemiologists) from the University of Edinburgh; and Bryan Grenfell from the University of Cambridge.

Improvements to the models developed during the UK 2001 outbreak proved long and arduous with just a few scientific gains (a testament to the quality of the models developed in the heat of the epidemic). The development of vaccination control strategies was far more successful with a publication in Nature.

Road or Euclidean distance?

It was clear during the UK 2001 epidemic that the closer a susceptible farm was to an infected premises (IP) the more likely is was to become infected. Estimates of the risk were captured in a transmission kernel shown in Fig. 1. This estimate was based on the Department of Environment, Food and Rural Affairs (Defra) tracing of infections. It has been shown to be biased towards close transmission probably because these are easier to confirm, however, newer estimates are not dissimilar.

In reality many transmission between farms occurred via the road network as demonstrated in Fig. 2. We wondered if, instead of a Euclidean-distance based transmission kernel, a road-distance based kernel might better explain infection between farms. Two road distance measures spring to mind: shortest route and quickest route.

We first got hold of the whole UK road network from Digimap, and converted their format into a format suitable for our study. On top of the road network we overlayed the position of all 180,000 livestock farms in the UK. We then calculated the shortest and quickest routes between all farms in the UK that are within 40km of each other (storage limitations meant that longer distances weren't contemplated). A great algorithm designed by Floyd and Warshall, can calculate the distance between all nodes in a network. The algorithm is O(N3); practically we could handle networks of about 10,000 nodes in one go.

To test if shortest or quickest routes were better predictors of transmission than Euclidean distance, we compared the actual distribution of road distances between potential transmission events to the distribution we would expect to see if road distance was not a risk factor. This was done using a bootstrap method. The result - no significant effect. So shortest or quickest route between farms is no better a predictor of transmission than Euclidean distance.

It was then pointed out to us by Cerian Webb of the University of Cambridge, that we could turn the question around; was Euclidean distance a better predictor of risk than shortest or quickest route. We did the analysis and surprisingly found that it was! Why? We don't really know.

The UK 2001 FMD virus is thought not to be particularly infectious when carried by wind, in contrast to the 1967 outbreak. This means that large geographical features that break the local connection between close farms may act as barriers to transmission. We were able to show that the M6 motorway that runs through Cumbria where the largest outbreak occurred probably did not act as a barrier. The Severn and Solway Firsth estuaries, however, were significant barriers to transmission. 

This work was published in BMC Veterinary Research.

Did farm infectiousness change over infectious period?

The most controversial issue during the UK 2001 epidemic was the pre-emptive culling of potentially uninfected animals on 3,370 farms contiguous to infected premises. Some people believe that contiguous culling had little effect in turning the epidemic around at the end of March 2001, whilst others believe the opposite. There seems little chance of there being a consensus anytime soon.

All models developed during the epidemic agreed that the control policy as implemented was not controlling the epidemic, and that a fully implemented IP/CP cull would. However, this result partially depends on the assumption that the infectiousness of infected farms did not change over their infectious periods. It has been argued that one would intuitively expect infectiousness to increase over infectious period because i) the spread of infection within a farm means more animals become infected, and ii) that the amount of virus excreted by animals rises exponentially over several days. However, the infectiousness of a farm depends on many other factors (e.g., biosecurity, management practices, shared personnel, equipment, roads and boundaries), and it is not known if these are more important in determining farm infectiousness than rising virus contamination of the environment.

We set out to see if the data on the UK 2001 epidemic could reveal changes in farm infectiousness. 

We fitted a mathematical model to the data that allowed for infectiousness to change over infectious period, and for a different infectiousness once the farm had been reported but not yet culled out (Fig. 3). The parameter ρ describes the linear increase in infectiousness from the first day on becoming infectious until the reporting day. The parameter μ describes the change in infectiousness after reporting compared to the first infectious day.

 We fitted the model to various regions of the UK that were affected by FMD. We also had to assume a value for latent period as this is not known with certainty for individual farms. The fits of the model to data give us estimates and 95% confidence intervals of the parameters. The results are shown in Fig. 4. On the face of it the results seem to suggest that ρ and μ are not significantly different from zero. This suggests that infectiousness did not change over infectious period.


We have had to make some assumptions, because
  1. we only have estimates of when infected farms were infected,
  2. we do not know the latent periods of infected farms,
  3. some infected farms may not have been reported because they were pre-emptively culled before reporting,
  4. some reported infected farms may not have been infected. 
So how might these assumptions affect our parameter estimates. To answer this we simulated epidemics with our model and artificially degraded the simulated data. These data were then fitted  to the model to obtain parameter estimates and confidence intervals. The results are shown in Fig. 5 and 6.

The conclusion is that the types of uncertainty we have in the data tend to cause estimates of ρ and μ to become non-significant. That is, poor data quality cause estimates of infectiousness over infectious period to be flat. Therefore, we cannot tell, using the UK 2001 epidemic data, if infectiousness changed over infectious period. This work was published in J. Roy. Soc. Interface.

Transmission and replication of FMD virus

With Richard Howey and Mark Woolhouse, we are studying how virus replicates within hosts by fitting mathematical models of viraemia data.
Document made with Nvu Created 25 August 06. Updated 26 August 07.