h the particles. The statistics for the trajectories of a large number of particles are computed by the models to forecast the dispersion. The sum of each virus mass expanding in time and space within a grid cell is counted as particle concentrations as shown in Figure 2. Advantages associated with these models are simplicity, flexibility and ability to produce relatively accurate results in atmospheric turbulence caused by complex terrain, etc. H[H8,16,33-36].

The position of a particle at time (t + Δt) along the x, y, and z directions is given by Equations (2)-(4), where U

Figure 2. Lagrangian approach: solve along the trajectory [37].

and V are the mean wind speed; U', V' and W' are velocity fluctuations [34,36].

(2)

(3)

(4)

Case study 5 for a case of FMD outbreaks in Australia; The paper illustrated 3 main structures of an integrated modelling approach to assess the risk of wind-borne spread of FMDV comprising an intra-farm virus production model, a wind transport and dispersion model, and an exposure-risk model. An atmospheric dispersion model selected in the study was the HYSPLIT model designed to use gridded wind data from numerical weather prediction models or 3-dimensional numerical analyses as input, or a combination of these. The grid span and the concentration grid spacing used for the simulations were about 150 km and 1 km, respectively. 8640 Lagrangian particles per day were released at 1 m height and a dry deposition velocity of 0.01 m×s−1 was assumed. The effect of biological ageing was considered by adopting a virus exponential decay constant. For the viability of the virus, the paper used a linear decrease in virus concentrations to account for the temperature effect and an exponential decrease for the humidity. The outputs of modelling were spatial plots of virus concentration at 1 m height in log10 TCID50×m−3. As a result, 10 of 139 farms surrounding the infected premise were rated as at medium or high risk, the closer farms having the higher risk. There were only a few cases in the study showing high risk at great distance. Seasons had a great influence in the result, as the large change was seen in the size of exposed areas and the number of farms at different levels of risk, according to the change of season. The wind speed and the height of the turbulent mixing layer, creating a measure of the turbulent mixing, were the main meteorological factors affecting the dispersion. This example also gave details about how to consider risk from the result of the atmospheric dispersion model. That will be explained further in the next topic, “Risk and viral production model” [16].

Case study 6 for a case of FMD outbreaks in UK; FMDV had spread in many countries throughout the UK as 54 outbreaks were recorded on March 26, 2001, at the epidemic’s peak. The paper presented the four atmospheric dispersion models (two for short-range and the other two for long-range models) and discussed the potential for disease spread in relation to the 4th and 6th outbreaks, in the early stages of the UK epidemic. Of the four atmospheric dispersion models, one was the Lagrangian dispersion model, NAME (Nuclear Accident ModEl). NAME was adapted to calculate downwind concentrations at 1 km intervals, same as another model compared in this case, the 10 km Gaussian plume model. NAME used 3-dimensional wind fields and other meteorological data from the Met Office’s numerical weather prediction model. NAME and the other long-range model showed similar results that were very low risk for long distance spread of FMD to Europe [8].

Case study 7 for a case of FMD outbreaks in Austria; two case studies using a Lagrangian particle model to investigate the airborne spread of FMDV were made with domains located in a hilly region in the northwest of the Styrian capital Graz, Austria, comprising a total of 2959 farms with 17,563 swine, 8842 goats and sheep and 39,203 cattle. Calculation of turbulence was based on a Monte Carlo method while the traditionally used Gaussian dispersion model was inapplicable due to mountainous terrain and time-varying meteorological conditions. Case studies illustrated the significance of local wind on the spread of virus under the influence of non-flat terrain. The study varied the different meteorological conditions on the two selected days. Four farms with different topographical environments were chosen. The study clearly demonstrated that Lagrangian particle models had superior advantages, i.e. extension of the range of application and applicability to nearly all real situations or phenomena (such as vertical wind shear, etc.) [8].

4. Risk and Viral Production Model

After the direction and concentration of FMDV spread is predicted, probabilities for the infection of farms exposed to airborne virus need to be evaluated. The important factors for the infection are the concentration of airborne virus, the air sampling capacity of the animal, the period of exposure, and the size of the herd. A commonly used concept to consider the risk of infection is the minimum infectious dose. The probability of infection exponentially increases with the size of the dose. The following binomial distribution presents the relationship of the probability (Pi) that an animal is infected when exposed to a given virus dose d in TCID50 and the probability that one TCID50 infects an animal (q) [16]:

(5)

As identified in this study, the probabilities that exposure to one infectious unit (IU) of virus would result in infection, estimated for cattle, sheep, and pigs, are 0.031, 0.045, and 0.003 respectively. Further from Pi, the probability that a group of animals becomes infected (Ph) also depends on the group size (n), given by:

(6)

In the case that more than one species is exposed to FMDV for multiple days, more factors must be considered, i.e. species (i), day (k), exposure dose (d), and number of animals of that species on the farm (n) as shown in the following relationship.

(7)

Based on these probabilities, Equations (5)-(7), a relative risk ranking—high, medium, low and very low— can be applied corresponding to probabilities of infection of >50, 10 - 50, 1 - 10 and <1%, respectively.

5. Interpretation of Dispersion Modelling Results

In risk assessment of FMD epidemics via wind-borne spread, reliable techniques and information are very necessary. Whenever possible, data based on actual records during the period of infection must be used. However, sometimes available data relies on estimations such as the exact date of lesions on infected animals, while sometimes it must rely on published values with limitations, which causes imperfection in the prediction [16, 38]. Numerical data producing a worst-case scenario can be optional to guarantee an action plan responding to an outbreak [26]. Consequently, output may be the value expressed as a maximum concentration for a short period, from one hour up to the entire emission period [19].

To carefully interpret the dispersion modelling results in order to develop a management plan, all possible incidences should be considered. For that, a sensitivity analysis of modelling results for assessing the potential for wind-borne spread of FMD to variations in key parameters controlling different physical and biological processes is imperative. Example parameters for such analysis from the literature are serotype of FMDV, biological ageing, weather change according to season, value of q or excretion rate, etc. [38].

6. Discussion

The selection of Gaussian or Lagrangian air dispersion models relies mainly on terrain characteristics affecting meteorological conditions. The Gaussian dispersion model provides a good estimation for aerosol spread of FMDV, and has been applied to the study of both short and long-range transmission. However, Gaussian plume or puff models have many restrictions with disregard to influential factors such as topography or changing wind directions. On the contrary, Lagrangian dispersion models can be applied to almost all inhomogeneous and time varying meteorological conditions as well as non-flat terrain. The model provides a more accurate approximation of the airborne spread of FMDV than the Gaussian dispersion model. Nevertheless, the Lagrangian dispersion model is very complex in use and requires a large number of weather input parameters which are timeconsuming and expensive to attain [8,9,39]. In any case, regardless of which type of air dispersion model is used, meteorological information to support the prediction acquired from both actual records and numerical weather prediction models is a serious factor affecting the accuracy of results [19].

7. Conclusion

To assist management of the potential spread of serious disease like FMD in cloven-hoofed animals, prediction models should be able to determine an accurate range and area of outbreak in advance as well as required minimum data can be obtained since error of prediction might cause serious impact. Selection of suitable model is one of the most important factors providing greater confidence in model outputs. Accuracy in the use of any models for the prediction of FMDV spread requires three essential considerations: 1) the amount of virus released into the atmosphere, 2) factors for virus viability, and 3) minimum quantity of virus causing infection. One of the main causes of FMDV infection via airborne transmission, especially for short-distances over land, is the population density of the target farm, as in the outbreaks in the UK in 1981 and Australia in Case study 1 - 2. For long-distance disease infection over the sea, the outbreak of FMD seems to depend on the coincidence of many factors. It is most likely when the following four circumstances are achieved simultaneously; 1) high output of virus predominantly associated with the outbreak of disease from pigs, 2) low dispersion of virus basically due to stable surface air and light winds, 3) high survival of virus mainly dependent on temperature and relative humidity, and 4) large numbers of susceptible livestock, especially for cows exposed to the virus for many hours [17,22]. Air dispersion modelling approaches to forecast the spread of FMDV are the main focus of this paper but to achieve the successful management and control in any outbreak of FMDV, interdisciplinary knowledge on veterinary, virology, epidemiology, and meteorology is required.

8. Acknowledgements

This research is financially supported by Changwon National University in 2011-2012.

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