Methods
Data
Full details on the different data sets used in the data analysis and model simulations can be found in the Text S1. For the modelling, livestock movement data for England and Wales in 2008 from both CTS and AMLS was used. Movements to slaughter were removed. CTS movements were batched, where individual movements with the same dates, departure and destination holdings were grouped together; AMLS data is already in a batch format. Holding location data (such as CPH, holding type and easting/northing co-ordinates) also came from AMLS and CTS whilst holding population data came from the 2008 census.
Model
The model [3] was individual-based at the level of the holding, and stochastic. Holdings were described by their dates of becoming exposed, infectious via movements, infectious via local spread, and removed, determined by the timings of movements and local spread events. Based on these dates, the holdings could be classed into one of the four states:
S - These are holdings without exposed or infectious animals.
H - These are farms containing animals exposed to infection, but with all these animals subject to isolation (triggered by the movement of animals onto the farm) until the movement restriction period has elapsed. The movement restriction period is 20 days for pigs, whereas for sheep and cattle, it is 6 days for England and Wales, and 13 days for Scotland [8]. These holdings do not constitute a source of further infection by either movement or local spread.
E - These holdings are similar to H, except with exposed animals not under movement restriction (e.g. it was infected by local spread), thus constituting a risk of further infection through off movements. These holdings are not yet infectious by local spread, but off-movements can carry exposed animals. A latent period of 3 days was used, within the range given by [6].
I - These are holdings containing infectious animals, after the latent period, which are a source of infection by both off-movement and local spread. FMD can spread rapidly within a population, infecting whole herds of cattle or pigs within one cycle of infection (ca 3 days). Therefore, we consider the entire holding as potentially infectious within this period after exposure [13].
Once infected, farms are assumed to remain infectious until the end of the simulation. Markets, however, are assumed to be disinfected and not continually occupied by livestock. Therefore in the model, infected markets re-enter the S state at the end of the following day, to allow for single overnight stays of livestock.
Epidemics were seeded by selecting a fixed small number of holdings (5 seeds are selected) from those with off-movements on the first day of the simulation. These are set to be infectious on this day. Consistent with the 2001 epidemic (e.g. [6]), the simulations were run for 28 days, beyond which it is assumed unlikely that an epidemic could persist without being identified. For the Pan Asia strain of FMD, clinical signs in cattle and pigs are typically detected quickly; it is more difficult to detect infection in sheep, but these are also less susceptible [14].
If a holding is exposed or infected, there are three ways in which the disease can spread to other holdings:
Movements: Only movements from exposed (E) or infected (I) holdings or markets can cause infection, and the risk of infection is assumed higher for movements of large numbers of animals. Different probabilities of infection, which are then weighted by the number of animals moved, are assumed for the movements of sheep compared to movements of cattle or pigs; movements of cattle or pigs from an infected holding are all assumed to be potentially infectious, whilst movements of sheep from an infected holding have a lower probability of infection. Furthermore, different probabilities of infection are assumed for movements from an infected market, as such movements are less certain to be infectious than those from an infected holding. Thus, for movements off a market (in the E or I state), μ was set at μm_sheep = 0.004 for sheep and μm_other = 0.02 for cattle and pigs. For other movements, we assumed a value of μother = 1.0 for cattle and pigs (all movements are potentially infectious) and μsheep = 0.02 for sheep. These movement parameters were based on the 2001 FMD epidemic and analysis of movements from infected holdings that resulted in infection spread [3].
Local Spread: Local spread unrelated to known movements from infected (I) holdings was modelled using a constant rate of generation of new infected holdings per day per infected holding β = 0.065. Local spread is assumed to be a combination of factors, including human and vehicle movements, possible airborne spread and nose-to-nose contact of livestock across boundaries. On each simulation day, a number of infectious contacts were selected for each infectious holding from a Poisson distribution with mean β, without replacement, considering only holdings reported as containing livestock in the agricultural census (or redistributed SOA population). Contacts were limited to a 10 km radius, and weighted according to distance d by p~e−ad, where a = 0.5 km−1. These local parameters were based on 2001 FMD epidemic sizes [3], [15]. Susceptible contacts become exposed on the current day of simulation. Infection by local spread negated the effect of any imposed standstill, and off movements from infected holdings were considered to potentially contain exposed animals.
Intra-SOA spread: Although movements within an SOA now need to be reported, very few within-SOA movements are recorded. This could be due to confusion on reporting requirements. Therefore, if one member of an SOA becomes infected, we assume that the rest may be infected too, due to unrecorded movements of infectious animals within the SOA. Upon infection of a holding on a given day, the model (optionally) identifies any other holdings within the same SOA, these then become infected and gain the same date of exposure as the source holding, but only become a source of further infection on the subsequent day (the day after the initial holding in SOA became infected), to allow time for distribution of animals within the SOA. In addition to the above, “one infected – all infected” option for within SOA spread, two other options for intra-SOA spread are available. In the model, all SOAs that were active on 01/01/2008 were considered in simulations throughout 2008. For CTS Links, all links that were active on 01/01/2008 were considered. These were then amalgamated into CTS Chains of linked holdings to form SOA like groups to create a worse case scenario of one infected – all infected in the CTS Chain. Three linked holding scenarios were considered in the model: (1) SOAs only; (2) CTS Links only, and (3) SOAs and CTS Links.
Epidemic simulations were run with starting times varied across the 2008 at 14-day intervals and repeated simulation at each starting point (simulations were repeated 400 times). The exact start day used in each simulation was subject to up to 14 days of jitter (i.e. a random value of up to 14 days is added to the defined start day to examine that period of the year rather than that specific day), in order to avoid unusual properties that might be associated with a single day. The distribution and prevalence of each 28-day simulated epidemic were recorded and divided by the number of seeds used.
Network Analysis
For the network analysis, a directed network of 73,926 nodes (premises) and 317,816 directed edges (movements) were created from the GB cattle movements for 2008, excluding movements to slaughter; markets were considered for this analysis and treated as farms. The shortest path between all pairs of connected nodes was then calculated, saving the source and destination nodes of the path. CTS Links active on 01/01/2008 were then added to the network as bi-directional edges, increasing the number of nodes and edges in the network by 20% and 4% respectively. The shortest path length between the saved pairs of source/destination nodes was then re-calculated in this expanded network.