Fig 1.
Schematic illustration of the multilevel model design.
The epizootic model uses two layers. Individual animals are resolved on the intrafarm layer, where disease spread acts between animals on the same farm. The disease model for individual animals, visible on the left in the figure, is described in Fig 2. In contrast, the smallest resolved units on the interfarm layer are the farms. At this layer, the disease is spread between farms by atmospheric transmission.
Table 1.
Disease model parameters for the duration of different disease stages (states).
Fig 2.
The disease model implemented for FMD.
An animal that becomes exposed to FMD is located at the top in the susceptible state. The infection model determines if the animal becomes infected and thereby is moved to the latent state or if it remains in the susceptible state. The animal is thereafter transferred through the model at a stochastic pace and path with probabilities determined by the set of model parameters depicted in the figure.
Table 2.
The disease model parameters for all three species.
Fig 3.
Disease transmission routes within farms.
(A) Illustration of a well-mixed group where all animals have equal connection with every other animal in the group. B) Three groups that are all separately well-mixed but have weaker connections to animals of the other groups.
Table 3.
The model parameters used in this study for the intrafarm disease spread of FMD.
Fig 4.
The development of FMD amongst the animals on an infected farm, i.e. intrafarm disease spread.
The disease is initiated with 5 infected and 95 uninfected animals in all cases. The disease develop quickest in the case with cattle and slowest for pigs.
Fig 5.
The meteorological preconditions are represented by local wind roses.
(A) One of the wind roses for the station Göteborg A plotted with polar coordinates. Wind speed and wind direction are represented by the radius and the angles, respectively. High values implies a high probability for that combination of wind speed and wind direction. Since the wind rose constitutes a probability distribution, the volume below the surface equals one. The figure clearly shows that the meteorological preconditions are anisotropic. (B) The 138 automatic meteorological stations of Sweden. Statistic datasets were gathered for each such station, together providing a proper description of the meteorological conditions of Sweden. Panel B uses a map from Natural Earth (public domain).
Fig 6.
The atmospheric stability influences the atmospheric transmission.
(A) The atmospheric stability changes over the day due to the influx of heat from the sun. (B) The exposure field following an atmospheric dispersion simulation, i.e. the exposure probability density, with a source at origin and a westerly wind with a speed of 2 ms-1 (at the height of 10 m) in the stability class E. The off-plume value is zero and is here set to 10-15 day m-3 for visualization reasons only.
Fig 7.
The farms in Sweden holding any of the three species cattle, pigs or sheep.
There is a significant dominance of farms in the southern part of Sweden while the inland of the north harbors very few farms due to low population and disadvantages preconditions. The map originates from Natural Earth (public domain).
Table 4.
Statistical measures extracted from the simulation results.
Fig 8.
The distributions of R0 values on a logarithmic scale for Sweden and Skåne for winter conditions.
The distributions are strongly heterogeneous with the majority of farms well below the epidemic threshold of R0 = 1 and a smaller fraction of farms with R0 in the order of 100. There is a significantly larger risk of epizootics in Skåne than on the national level as the right panel reveals.
Fig 9.
The geographic distribution of the basic reproduction number R0 during winter.
Panel A, the values for all of the 29 729 farms have been applied to a high resolved grid using a Gaussian kernel with a standard deviation of 1.25 km to render a geographical representation of the basic reproduction number. Panel B, the fraction of farms with basic reproduction number that exceeds 1 has been counted in each cell of a grid. The borders are provided Natural Earth (public domain).
Fig 10.
Extracted spatial and temporal distributions of the disease transmission.
(A) The probability for disease spread as a function of distance. The low value for distances close to zero reflects the fact that farms are in general rarely located in close proximity to each other. The inset shows the same data with a correction for the increase in area, and therefore the number of farms, with distance. (B) The mean effective reproduction number for all seasons as function of the number of the culling delay. The points form a smooth sigmoidal curve to which logistic functions are fitted and displayed with dashed curves. For each culling time investigated, all farms were used as epizootic seeds during 100 simulations for each season. This implies that each point for Sweden is the mean of 12 million simulations, which results in low numerical uncertainties. The corresponding number for Skåne is 1.6 million. The curves for the set of farms without pigs are depicted with dashed lines. In this case, neither Sweden nor Skåne reached the epidemic threshold.